Algebra: Geometry Word Problems

Geometry word problems involves geometric figures and angles descrihed in words. You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

Geometry Word Problems Involving Area

Example:

A rectangle is 4 times as long as it is wide. If the length is increased by 4 inches and the width is decreased by 1 inch, the area will be 60 square inches. What were the dimensions of the original rectangle?

Solution:

Step 1: Assign variables:

Let x = original width of rectangle
Sketch the figure

Step 2: Write out the formula for area of rectangle.

A = lw

Step 3: Plug in the values from the question and from the sketch.

60 = (4x + 4)(x –1)

Use distributive property to remove brackets
60 = 4x² – 4x + 4x – 4

Put in Quadratic Form
4x² – 4 – 60 = 0
4x² – 64 = 0

This quadratic can be rewritten as a difference of two squares
(2x)² – (8)² = 0

Factorize difference of two squares
(2x)² – (8)² = 0
(2x – 8)(2x + 8) = 0

We get two values for x.

Since x is a dimension, it would be positive. So, we take x = 4

The question requires the dimensions of the original rectangle.
The width of the original rectangle is 4.
The length is 4 times the width = 4 × 4 = 16

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

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