Maths Worksheet for Kids- Pythagorean Theorem Worksheet

The Pythagoras Theorem applied in a right-angled triangle states that the square of the side hypotenuse will be equal to the sum of the squares of the base and the perpendicular.

Let's solve some questions for further understanding -

Questions:

1. Identify the length of hypotenuse in the given triangle -

Image - An Image of a Triangle

2. Pythagoras' theorem is applicable in which kind of triangles?

3. Solve for an in the given triangle -

Image - An Image of a Triangle

4. Is the given figure a right-angled triangle ?

Image - An Image of a Triangle

5. Find the value of the missing side.

Image - An Image of a Triangle

6. Find the length of the hypotenuse. 

Image - An Image of a Triangle

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

Image - An Image of a Triangle

8. Is the following Pythagorean Triplet correct?

3, 5 and 7

9. Solve for c in the given triangle -

Image - An Image of a Triangle

10. In the below given right triangle, find the value of y.

Image - An Image of a Triangle

11. In a right triangle, the longest side is 8 cm. One of the remaining sides is 4√3 cm long. Find the length of the other side.

12. What is the value of the missing side of the triangle?

Image - An Image of a Triangle

13. ABC is a right triangle. AC is its hypotenuse. The length of side AB is 2√5. Side BC is twice side AB. Find the length of AC.

14. Find the value of x.

Image - An Image of a Triangle

15. Is ∆ABC a right-angled triangle, where AB = 5cm, BC = 10cm, AC = 15cm?

Answers -

1. 7.2, the length of the hypotenuse in the given triangle is 7.2.

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

3. Given, b=12 and c= 15

a2+b2=c2

a2+ 144 =225

Subtract 144 from each side to get:

144 - 144 + a2 = 225 - 144

a2 = 225 - 144 ⇒ a2 = 81

⇒ a = √81

a = 9

4. Yes, the given triangle is a right angled triangle.

5. By Pythagoras theorem, a2+b2=c2

Let b=9 c=12

144 - 81 =a2 ⇒ 63 = a2

√63 = a

Therefore, the length of the missing side is √63.

6. 10in.

7. By Pythagoras theorem, a2+b2=c2

Let a=6 b=7 c=9

36 + 49 = 81 ⇔ 9 x 9 = 81

Therefore, LHS≠RHS

Hence, the given triangle is not a right angle triangle.

8. By Pythagoras theorem, a2+b2=c2

Let a=3 b=5 c=7

9 + 25 = 34

7 × 7 = 49

Therefore, LHS≠RHS

Hence, 3, 5 and 7 are not correct Pythagorean triplets.

9. Given, a=11 b=15

By Pythagoras theorem, 

a2+b2=c2

121 + 225 = c2

346 = c2

c = √346m

10. By Pythagoras theorem we get,

z2=x2+y2

Now, directly substituting the values

⇒ 169 = 25 + y2

⇒ y2 = 144 ⇒ y = 12

Hence, the value of y is 12.

11. 4cm.

12. By Pythagoras theorem, a2+b2=c2

Let a=3 b= 6

9 + 36 = c2 ⇒ 45 = c2

√45 = c

Therefore, the length of the missing side is √45cm.

13. AC = 10

14. By the pythagoras theorem, Hypotenuse2 = Base2 + Perpendicular2

x2 = 64+36 = 100

x = 10

Therefore, the value of x is 10.

15. If ∆ABC is a right-angled triangle, then AB2+BC2=AC2

AB = 5, BC =10, AC = 15

AB2 + BC2 = 25 + 100 = 125

AC2 = 225

Since, AC2 ≠ AB2 + BC2

Hence, ABC is not a right-angled triangle.

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