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Algebra: Geometry Word Problems - Area

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How to solve geometry word problems that involve geometric figures and angles described 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


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?


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.

The following video gives another example of geometry word problem that involves area.
Example: A rectangle is twice as long as it is wide. If the area of the rectangle is 98 cm2, find its dimensions.
Writing quadratic equations to solve word problems: Area of a triangle
Example: The height of a triangles is 3 cm more than its base. The area of the triangle is 17 cm2. Find the base to nearest hundredth of a cm.

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