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

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

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