Worksheet on Pythagorean Theorem

Practice the questions given in the worksheet on Pythagorean Theorem. We know, in a right angled triangle the square of the hypotenuse is equal to the sum of the squares of its remaining two sides.

Hypotenuse\(^{2}\) = Perpendicular\(^{2}\) + Base\(^{2}\)

1. The side of the triangle are of length 7.5 m, 4 m, 8.5 m. Is this triangle a right triangle? If so, which side is the hypotenuse?

2. In ∆ABC right angled at A. if AB = 10 m and BC = 26 m, then find the length of AC.

3. In ∆XYZ right angled at Y. find the length of the hypotenuse if the length of the other two sides is 1.6 cm and 6.3 cm.

4. If the square of the hypotenuse of an isosceles right triangle is 98cm\(^{2}\), find the length of each side.

5. A tree broke from a point but did not separate. Its top touched the ground at a distance of 24 m from its base. If the point where it broke is at the height of 7 m from the ground, what is the total height of the tree?

6. A ladder 13 m long when set against the wall of house just reaches a window at a height of 12 m from the ground. How far is the lower end of the ladder from the base of the wall?

7. Find the perimeter of the rectangle whose length is 24 cm and diagonal is 26 cm.

8. The diagonal of the rhombus is 24 m and 10 m. find the perimeter.

9. One of the diagonals of the rhombus is 3 cm and each side is 2.5 cm. Find the length of the other diagonal of the rhombus.

10. A ladder 8.5 m long rests against a vertical wall with its foot 4 m away from the wall. How high up the wall the ladder reach?

11. The height of two towers is 150 m and 136 m respectively. If the distance between them is 48 m, find the distance between their tops.

12. The base of an isosceles triangle is 24 cm and the two equal sides are 37 cm each. Find the altitude AD of the triangle.

13. ∆PQR is an isosceles right triangle right angled at R. Prove that PQ\(^{2}\) = 2PR\(^{2}\).

14. Starting from a place, two person travel in bicycles along two perpendicular roads at speed of u km/hr and v km/hr. Find the distance between their positions after t hours.

Answers for the worksheet on Pythagorean Theorem are given below to check the exact answers of the above questions on Pythagoras.


1. Yes, hypotenuse = 8.5 m

2. 24 m

3. 6.5 cm

4. 7 cm

5. 32 m

6. 5 m

7. 68 cm

8. 52 m

9. 4 cm

10. 7.5 m

11. 50 m

12. 35 cm

14. \(t\sqrt{u^{2} + v^{2}}\)

Math Home Work Sheets

7th Grade Math Problems

8th Grade Math Practice

From Worksheet on Pythagorean Theorem to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. 2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic

    Dec 06, 23 01:23 AM

    2nd Grade Math Worksheet
    2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.

    Read More

  2. Rupees and Paise | Paise Coins | Rupee Coins | Rupee Notes

    Dec 04, 23 02:14 PM

    Different types of Indian Coins
    Money consists of rupees and paise; we require money to purchase things. 100 paise make one rupee. List of paise and rupees in the shape of coins and notes:

    Read More

  3. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Dec 04, 23 01:50 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More