Maths Worksheet for Kids- Pythagorean Theorem Find the Missing Leg

According to the Pythagoras theorem, the square of the hypotenuse equals the sum of the squares of the remaining two sides in a right-angled triangle.

Let's solve some questions for further understanding -

Questions:

1. Find the value of y in the given triangle.

Image - an image of a triangle

2. Identify the length of the hypotenuse?

Image - an image of a triangle

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

Image - an image of a triangle

4. Find the value of x.

Image - an image of a triangle

5. Find the value of c.

Image - an image of a triangle

6. Find the value of the missing side.

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7. 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.

8. Use Pythagoras Theorem to find the missing side.

Image - an image of a triangle

9. Find the third side of the given triangle.

Image - an image of a triangle

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

11. What is the length of the hypotenuse in the given triangle?

Image - an image of a triangle

12. Find the missing side by using Pythagoras Theorem.

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13. What is the length of the hypotenuse of the given triangle ?

Image - an image of a triangle

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

15. Find the length of the hypotenuse. 

Image - an image of a triangle

Answers -

1. 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.

2. 5.1mm

3. By Pythagoras Theorem, a2+b2=c2

Let a=3 b= 6

9 + 36 = c2 ⇒ 45 = c2

√45 = c

4. By the Pythagoras Theorem, Hypotenuse2 = Base2 + Perpendicular2

x2 = 64+36 = 100

x = 10

Therefore, the value of x is 10.

5. By Pythagoras Theorem, a2+b2=c2

Let a=5 b=7

25 + 49 = c2 ⇒ 74 = c2

√74 = c

Therefore, the value of c is √74.

6. By Pythagoras Theorem, a2+b2=c2

Let a=5 b=5

25 + 25 =c2 ⇒ 50 = c2

√50 = c

7. 4cm.

8.  By Pythagoras Theorem, a2+b2=c2

Let c =19 b=17

a2 + 289 = 361 ⇒ 72 = a2

√72 = a

9. Given: a = 3, c = 5

Putting the values in the Pythagoras Formula: a2+b2=c2

9 + b2 = 25

b2 = 25 − 9 = 16 

b = 4

Therefore, the third side is 4.

10. 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.

11. 9.6m.

12. By Pythagoras Theorem, a2+b2=c2

Let c =20 b=10

a2 + 100 = 400 ⇒ 300 = a2

√300 = a

13. Pythagoras Formula: a2+b2=c2

Let AB = a = 20, BC = b = 21

Putting values in the formula

400 + 441 = c2

841 = c2

c = 29 cm

14. AC = 10

15. 10in

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