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# Word Problems Involving Geometric Shapes Practice Problems

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By McGraw-Hill Professional
Updated on Sep 27, 2011

## Geometry Word Problems Practice Problems

### Set 1: Introduction to Geometry Word Problems - Rectangles and Squares

To review word problems involving geometric shapes, go to Word Problems Involving Geometric Shapes Help

#### Practice

1. The diameter of a square is 60 feet. What is the length of its sides?
2. A rectangle has one side 14 cm longer than the other. Its diameter is 34 cm. What are its dimensions?
3. The length of a rectangle is 7 inches more than its width. The diagonal is 17 inches. What are its dimensions?
4. The width of a rectangle is three-fourths its length. The diagonal is 10 inches. What are its dimensions?
5. The diameter of a rectangular classroom is 34 feet. The room’s length is 14 feet longer than its width. How wide and long is the classroom?

#### Solutions

When there is more than one solution to an equation and one of them is not valid, only the valid solution will be given.

1. Let x represent the length of each side (in feet). The diagonal is 60 feet, so D = 60. The formula D 2 = L 2 + W 2 becomes 60 2 = x 2 + x 2.

The length of the square’s sides is feet, or approximately 42.4 feet.

2. The length is 14 cm more than the width, so L = W + 14. The diameter is 34 cm, so D = 34. The formula D 2 = L 2 + W 2 becomes 34 2 = ( W + 14) 2 + W 2 .

The width is 16 cm and the length is 16 + 14 = 30 cm.

3. The length is 7 inches more than the width, so L = W + 7. The diagonal is 17 inches. The formula D 2 = L 2 + W 2 becomes

The rectangle’s width is 8 inches and its length is 8 + 7 = 15 inches.

4. The width is three-fourths its length, so . The diagonal is 10 inches, so the formula D 2 = L 2 + W 2 becomes .

The rectangle’s length is 8 inches and its width is inches.

5. The classroom’s length is 14 feet more than its width, so L = W + 14. The diameter is 34 feet. The formula D 2 = L 2 + W 2 becomes 34 2 = ( W + 14) 2 + W 2.

The classroom is 16 feet wide and 16 + 14 = 30 feet long.

### Set 2: Triangles and Miscellaneous Shapes

To review quadratic applications, go to Word Problems Involving Geometric Shapes Help

#### Practice

1. The area of a triangle is 12 in 2. The length of its base is two-thirds its height. What are the base and height?
2. The area of a triangle is 20 cm 2. The height is 3 cm more than its base. What are the base and height?
3. The sum of the base and height of a triangle is 14 inches. The area is 20 in 2.  What are the base and height?
4. The hypotenuse of a right triangle is 85 cm long. One leg is 71 cm longer than the other. What are the lengths of its legs?
5. The manufacturer of a food can wants to increase the capacity of one of its cans. The can is 5 inches tall and its diameter is 6 inches. The manufacturer wants to increase the can’s capacity by 50% and wants the can’s height to remain 5 inches. How much does the diameter need to increase?
6. A pizza restaurant advertises that its large pizza is 20% larger than the competition’s large pizza. The restaurant’s large pizza is 16 inches in diameter. What is the diameter of the competition’s large pizza?

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