Introduction to geometry word problems

Geometry is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. Initially the body of the practical knowledge is concerning with the lengths, areas, and volumes. (Source:wikipedia)

In this article we shall discuss about geometry word problems.

Geometry Word Problems Involving Area:

A rectangle is 4 times as extended as it is wide. If the measurement lengthwise is more than 4 inches and the width is less than 1 inch, the area will be 60 square inches. What were the dimensions of the original rectangle?

Solution:

Let x = original width of rectangle

Area of the rectangle is

A = l w

Plug in the values from the question

60 = (4x + 4) (x –1)

Use distributive property to remove brackets

60 = 4x2 – 4x + 4x – 4

Put in quadratic formula 4x2 – 4 – 60 = 0

4x2 – 64 = 0

This quadratic written as a difference of two squares

(2x) 2 – (8)2 = 0

Factorize Difference of two squares are

(2x) 2 – (8)2 = 0

(2x – 8)(2x + 8) = 0

Therefore the values for x is

Since x is a dimension, it would be positive.

So, we take x = 4

The question wants the dimensions of the original rectangle.

The width of the given rectangle is 4.

The length is 4 times the width = 4 × 4 = 16

Answer: The dimensions of the rectangle are 4 and 16.

Geometry Word Problems Involving Perimeter:

 A triangle has a perimeter of 50. If 2 of its sides are equivalent and the third side is five more than the equivalent sides, what is the length of the third side?

Solution:

Let x = length of the equal side

The formula for perimeter of rectangle

P = sum of the three sides

Plug in the values from the question

50 = x + x + x+ 5

Combine like terms

50 = 3x + 5

Isolate variable x

3x = 50 – 5

3x = 45

x =15

The question requires length of the third side.

The length of third side is = 15 + 5 =20

Answer: The length of third side is 20

Practice Geometry Word Problems:

A triangle has a perimeter of 80. If 2 of its sides are equivalent and the third side is five more than the equivalent sides, what is the length of the third side?
                   Answer: The length of third side is 30

A triangle has a perimeter of 95. If 2 of its sides are equivalent and the third side is five more than the equivalent sides, what is the length of the third side?
                   Answer: The length of third side is 35