Given:
a.) A plot of land for sale has a width of x ft. and a length that is 8 ft. less than its width.
b.) A farmer will only purchase the land if it measures 240 ft.
From the given description of the measurement of the land, we generate the following equations:
Width = w
Length = w - 8
Area of the Land = 240 ft.^2
Area = Width x Length
240 = (w)(w - 8)
240 = w^2 - 8w
w^2 - 8w - 240 = 0
Question 1: Create an equation in terms of w that models this situation.
Answer: 240 = w^2 - 8w
Factoring out 240 = w^2 - 8w, we get:
240 = w^2 - 8w
w^2 - 8w - 240 = 0
w^2 - 8w - 240 = 0 → (w - 20)(w + 12) = 0
First possible measure of the width,
w - 20 = 0
w = 20 ft.
Second possible measure of the width,
w + 12 = 0
w = -12 ft.
A dimension must never be a negative value, therefore, the width must be equal to 20 ft.
Let's determine the length,
Length = w - 8
= 20 - 8
Length = 12 ft.
Summary:
The equation that models the situation: 240 = w^2 - 8w or w^2 - 8w = 240
The measure of the length = 12 ft.
The measure of the width = 20 ft.