pythagoras problem solving pdf

Pythagorean Theorem Exercises

Pythagorean theorem practice problems with answers.

There are eight (8) problems here about the Pythagorean Theorem for you to work on. When you do something a lot, you get better at it. Let’s get started!

Here’s the Pythagorean Theorem formula for your quick reference.

Note: drawings not to scale

Problem 1: Find the value of [latex]x[/latex] in the right triangle.

[latex]10[/latex]

Problem 2: Find the value of [latex]x[/latex] in the right triangle.

[latex]4\sqrt 7 [/latex]

Problem 3: Find the value of [latex]x[/latex] in the right triangle.

[latex]3[/latex]

Problem 4: The legs of a right triangle are [latex]5[/latex] and [latex]12[/latex]. What is the length of the hypotenuse?

[latex]13[/latex]

Problem 5: The leg of a right triangle is [latex]8[/latex] and its hypotenuse is [latex]17[/latex]. What is the measure of its other leg?

[latex]15[/latex]

Problem 6: Suppose the shorter leg of a right triangle is [latex]\sqrt 2[/latex]. The longer leg is twice the shorter leg. Find the hypotenuse.

[latex]\sqrt {10} [/latex]

Problem 7: The hypotenuse of a right triangle is [latex]4\sqrt 2[/latex]. If the longest leg is half the hypotenuse, what is the length of the shortest leg?

[latex]2\sqrt 6[/latex]

Problem 8: Find the value of [latex]x[/latex] of the right isosceles triangle.

[latex]\sqrt 6[/latex]

You may also be interested in these related math lessons or tutorials:

Pythagorean Theorem

Pythagorean Triples

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How to Solve Pythagorean Theorem Problems? (+FREE Worksheet!)

In mathematics, the Pythagorean Theorem is the relationship between three sides of a right triangle.

Related Topics

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Step by step guide to solve Pythagorean Theorem problems

• We can use the Pythagorean Theorem to find a missing side in a right triangle.

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The pythagorean theorem – example 1:.

Right triangle ABC has two legs of lengths \(9\) cm (AB) and \(12\) cm (AC). What is the length of the third side (BC)?

Use Pythagorean Theorem: \(\color{blue}{a^2+b^2= c^2}\) Then: \(a^2+b^2= c^2 →9^2+12^2= c^2 →81+144=c^2\) \(c^2=225 →\) \(c=\sqrt{225}=15\) \(cm\) → \(c=15 cm\)

The Pythagorean Theorem – Example 2:

Use Pythagorean Theorem: \(\color{blue}{a^2+b^2= c^2}\) Then: \(a^2+b^2= c^2 →8^2+6^2= c^2 →64+36=c^2\) \(c^2=100 →\) \(c=\sqrt{100}=10\) → \(c=10\)

The Pythagorean Theorem – Example 3:

Find the hypotenuse of the following right triangle.

Use Pythagorean Theorem: \(\color{blue}{a^2+b^2= c^2}\) Then: \(a^2+b^2= c^2 →3^2+4^2= c^2 →9+16=c^2\) \(c^2=25 →\) \(c=\sqrt{25}=5\) → \(c=5\)

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The pythagorean theorem – example 4:.

Right triangle ABC has two legs of lengths \(6\) cm (AB) and \(8\) cm (AC). What is the length of the third side (BC)?

Use Pythagorean Theorem: \(\color{blue}{a^2+b^2= c^2}\) Then: \(a^2+b^2= c^2 →6^2+8^2= c^2 →36+64=c^2\) \( c^2=100 →\) \(c=\sqrt{100}=10\) \(cm\) → \(c= 10 cm\)

Exercises for Solveing the Pythagorean Theorem

Find the missing side in each right triangle., download pythagorean relationship worksheet.

• \(\color{blue}{13}\)
• \(\color{blue}{5}\)
• \(\color{blue}{15}\)
• \(\color{blue}{8}\)

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by: Effortless Math Team about 4 years ago (category: Articles , Free Math Worksheets )

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• Maths Worksheet for Kids- Pythagorean Theorem Practice Worksheet

Maths Worksheet for Kids | Pythagorean Theorem Practice Worksheet - Download Free PDF with Solutions

If you want to learn all about right-angled triangles and find the leg and base values best, you can download and refer to the Pythagorean Theorem Practice Worksheet from Vedantu. These worksheets are available in PDF format to guide the students about basic concepts related to the Pythagorean theorem. Students of KG-3 can download the worksheets and practice the questions from there to gain better knowledge about the topics in the first place.

The printable PDF worksheets have different exercises students can solve to build a strong conceptual foundation about the theorem. There are many different types of Pythagoras Theorem Questions in these exercises to make sure that students can get a good grasp of the topic in the first place. Hence, students should download the worksheets and learn the type of questions provided there.

Access Worksheet for Maths KG-2 Pythagorean Theorem Practice

In Maths, the Pythagorean theorem states that “In a right triangle, the square of the hypotenuse equals the sum of squares of the remaining two sides.”

Let’s solve some questions for further understanding -

Identify the length of the hypotenuse in the given triangle -

Image - An Image of a Triangle  

Identify the length of the perpendicular in the given triangle -

Image - An Image of a Triangle

Is the given figure a right-angled triangle?

Identify the length of the base in the given triangle -

Image - an Image of a Triangle

Use Pythagoras' Theorem to check whether the given triangle is a right-angle triangle or not.

Find the value of x.

Pythagoras' theorem is applicable in which type of triangles?

[Acute triangles, right-angled triangles, or obtuse triangles]

Is the given triangle right-angled?

Find the length of the hypotenuse in the given triangle.

Find the length of the hypotenuse in the given triangle using Pythagoras' theorem.

Image - an image of a triangle

Does the Pythagorean theorem apply to right triangles?

Is the following Pythagorean triplet correct?

Solve for an in the given triangle -

Solve for c in the given triangle -

8.1m, the hypotenuse length in the given triangle is 8.1m.

4cm 6cm, the perpendicular length in the given triangle can be 4cm or 6cm.

Yes, the given triangle is right-angled.

9cm or 12cm. The length of the base in the given triangle can be 9cm or 12cm.

By pythagoras theorem, a 2 + b 2 = c 2

Let a=9 b=5 c=10.3

81 + 25 = 106 ⇔ 10.3 × 10.3 = 106 approx.

Therefore, LHS=RHS

Hence, the given triangle is a right-angle triangle.

Given a=6 b=8

36 + 64 = c 2 ⇒ 100 = c 2

Hence, the value of x is 10.

Pythagoras' theorem is applicable only in right-angled triangles.

No, the given triangle is not right-angled.

9.3cm the hypotenuse length in the given triangle is 9.3cm.

By Pythagoras' theorem, a 2 + b 2 = c 2

Let a=3 b=7

9 + 49 = c 2 ⇒ 58 = c 2

Hence, the hypotenuse length is √58.

Yes, the Pythagorean Theorem applies to all right-angled triangles. 

By Pythagoras theorem, a 2 + b 2 = c 2

Let a=3 b=4 c=5

Hence, 3, 4 and 5 are correct Pythagorean triplets.

Given, b=12 and c= 15

a 2 + b 2 = c 2

a 2 + 144 =225

Subtract 144 from each side to get:

144 - 144 + a 2 = 225 - 144

a 2 = 225 - 144 ⇒ a 2 = 81

Given, a=3 b=4

By Pythagoras’ theorem, 

32 + 42 = c 2

3×3 + 4×4 = c 2

9 + 16 = c 2

Did You Know?

Were you aware that Pythagoras, the person who is credited for discovering the Pythagorean Theorem, claimed to have already lived four lives? Yes, the renowned mathematician claimed that he remembered the previous four lives that he had lived. Apart from that, he was also supposedly a great friend to animals and loved them very much.

Importance of Pythagorean Theorem Practice Questions for Students 

Students of KG-3 will have to complete their Maths syllabus to gain a good understanding of the topics. In that process, the worksheets for the Pythagorean theorem can help them out. The concepts have been explained very well in the worksheets. Additionally, there are some very important questions hand-picked by the experts at Vedantu for a better student learning experience. They can score good marks on these worksheets.

The worksheets contain numerical problems, Pythagorean theorem word problems, real-time problems, and much more. By repeatedly solving the questions from the worksheets, students will gain a good understanding of the different topics and processes explained here. Students can rely on the authenticity of the worksheets as the questions are on par with the school board's standards. Students will also find the Pythagoras theorem chart depictions and learn how to create them.

Benefits of Pythagoras Theorem Practice Questions 

Students can understand a lot about the topic by solving the questions from the worksheets. 

Finding out the values related to the aspects of a right-angled triangle has been explained so that students can learn how to solve these questions. 

The experts at Vedantu have provided an easy and simple explanation for all the solutions. Students will be able to understand the solutions without any additional effort easily. 

Overall, the worksheets from Vedantu are resourceful study materials that will help the students prepare for their exams.

Students can rely on the authenticity of the worksheets and the solutions as they are entirely accurate and contain a lot of information that will be useful for students.

Download Pythagorean Theorem Worksheets From Vedantu

Your chance to download the Pythagorean triples examples with answers is right here. Get your hands on these helpful worksheets and better understand the concepts. These worksheets will help you practice appropriately so you can score some good marks in the examinations.

FAQs on Maths Worksheet for Kids- Pythagorean Theorem Practice Worksheet

1. What is the Pythagorean theorem?

According to the Pythagoras theory, the square of the hypotenuse of a right-angled triangle will be the sum of the squares of the base and the perpendicular of the triangle.

2. Where can I use the Pythagoras theorem?

You can use the Pythagoras theorem to solve different questions related to the area and perimeter of a right-angled triangle.

3. Can I score good marks in Maths with the Pythagorean theorem worksheet?

Yes, you can definitely score some good marks in your exams if you practice solving the questions regularly from the worksheets for the Pythagorean theorem.

4. How can I use the practice problems to score good exam marks?

After downloading the Pythagorean theorem practice problems, students can go ahead and practice the problems again and again, to get better at them.

5. Are the worksheets utterly free of cost?

Yes, the Pythagorean theorem practice worksheets are free of cost and can be downloaded from the official website of Vedantu.

Pythagoras Textbook Exercise

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Pythagoras problem solving questions

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

31 January 2018

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