WORD PROBLEMS USING PYTHAGOREAN THEOREM WORKSHEET

Problem 1 :

A rectangle has sides of length 7 cm and 3 cm. Find the length of its diagonals.

Solution

Problem 2 :

The longer side of the rectangle is double the length of the shorter side. If the length of a diagonal is 10 cm, find the dimension of the rectangle.

Solution

Problem 3 :

A rectangle with diagonals of length 30 cm has sides in the ratio 3 : 1. Find the 

(a) Perimeter   (b) Area of the rectangle. 

Solution

Problem 4 :

A rhombus has sides of length 7 cm. One of the diagonals is 10 cm long. Find the length of the other diagonal.

Solution

Problem 5 :

A square has diagonals of length 8 cm. Find the length of the sides.

Solution

Problem 6 :

A rhombus has diagonal of length 4 cm and 6 cm. Find the perimeter.

Solution

Problem 7 :

An equilateral triangle has sides of 6 cm

(a)  Find the length one of its altitude.

(b)  Find the area of the triangle.         Solution

Problem 8 :

An isosceles triangle has equal sides of length 8 cm and the base of length 6 cm.

(a)  Find the altitude of the triangle

(b)  Find the area of the triangle             Solution

Answer Key

1)  AC = 7.61 cm

2)  4√5 cm

3)  a)  24√10 cm

b)  270 cm2

4)   12√6 cm

5)  4√2

6)  4√13

7)  a)  AD = 3√3

b)  9√3

8)  a)  AD = √55

b)   4√55 cm2

For each triangle find the missing length. Round your answer to the nearest tenth. Then find the area and the perimeter.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Find a third number so that the three numbers form a right triangle:

9 , 41

Solution

Problem 4 :

Ms. Green tells you that a right triangle has a hypotenuse of 13 and a leg of 5. She asks you to find the other leg of the triangle. What is your answer?

Solution

Problem 5 :

The sides of a triangle have lengths x, x + 5, and 25. 

If the length of the longest side is 25, what value of x makes the triangle a right triangle?

Solution

Problem 6 :

A 22 foot ladder lean against a shed reaching a height of x feet. The base of the ladder is 10 feet from the shed.

Solution

Answer Key

1)  x = 8.48

2)  x = 13.92

3)  x = 40

4)  x = 12

5)  x = 15

6)  x = 19.6 feet

The following figures are not drawn to scale. Which of the triangles are right angled?

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Answer Key

1) Not a right triangle

2)  A right triangle

3)  not a right triangle.

4)  not a right triangle.

5)  a right triangle

6)  a right triangle.

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