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

Problem 9 :

The backboard of the basketball hoop forms a right triangle with the supporting rods, as shown. Use the Pythagorean Theorem to approximate the distance between the rods where they meet the backboard.

Solution

Problem 10 :

The fire escape forms a right triangle, as shown. Find the distance between the two platforms.

Solution

Problem 11 :

Approximate the wingspan of the butterfly.

Solution

Problem 12 :

The legs of a right triangle have lengths of 28 meters and 21 meters. The hypotenuse has a length of 5x meters. What is the value of x ?

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

Problem 7 :

A small shelf sits on two braces that are in the shape of a right triangle. The leg (brace) attached to the wall is 4.5 inches and the hypotenuse is 7.5 inches. The leg holding the shelf is the same length as the width of the shelf. What is the width of the shelf?

Solution

Problem 8 :

Can a right triangle have a leg that is 10 meters long and a hypotenuse that is 10 meters long? Explain.

Solution

Problem 9 :

One leg of a right triangular piece of land has a length of 24 yards. The hypotenuse has a length of 74 yards. The other leg has a length of 10x yards. What is the value of x?

Solution

Problem 10 :

You built braces in the shape of a right triangle to hold your surfboard. The leg (brace) attached to the wall is 10 inches and your surfboard sits on a leg that is 24 inches. What is the length of the hypotenuse that completes the right triangle?

Solution

Problem 11 :

Laptops are advertised by the lengths of the diagonals of the screen. You purchase a 15-inch laptop and the width of the screen is 12 inches. What is the height of its screen?

Solution

Problem 12 :

In a right isosceles triangle, the lengths of both legs are equal. For the given isosceles triangle, what is the value of x?

Solution

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

Problem 1 :

Solution

Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 5 :

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Problem 6 :

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Problem 7 :

Determine the area and perimeter of the triangle shown on the right.

Solution

Problem 8 :

A rectangular park has a straight path from one corner to the opposite corner. If the park has dimensions of 2 km by 1.4 km, determine the length of the path.

Solution

Problem 9 :

A 12-foot ladder is leaned against the side of a building. If the bottom of the ladder rests 3 feet from the wall, determine the height at which the top of the ladder rests on the wall.

Solution

Problem 10 :

When a triangle is inscribed in a semicircle, a right angle is always formed at the point on the circular arc. Calculate the area of the shaded region in the diagram below.

Solution

Problem 11 :

Determine the perimeter of the triangle shown on the right.

Solution

Problem 12 :

A television screen has a width-to-height ratio of 16:9. If the diagonal of the screen is 65 inches, determine its width and height.

Solution