Answer:
Length = 12 in
Width = 9 in
Explanations:
Let the length of the scrapbook be represented as L
Let the width of the scrapbook be represented as W
The scrapbook is 3 in longer than its width.
This can be represented mathematically as:
L = W + 3........................(1)
Since the length of the scrapbook is longer than the width, the scrapbook has a rectangular shape.
Area of a Rectangle = Length x Width
Let the area be represented as A
A = L X W........................(2)
The Area is 108 in²
A = 108 in²
Put the value of A into equation (2). The equation becomes:
108 = L X W...................(3)
Substitute equation (1) into equation (3):
108 = (W + 3) x W
108 = W² + 3W
W² + 3W - 108 = 0
W² -9W + 12W - 108 = 0
W(W - 9) + 12(W - 9) = 0
(W + 12)(W - 9) = 0
W + 12 = 0
W = -12
W - 9 = 0
W = 9
Since the width of a scrapbook cannot be negative, we will choose W = 9 in
Substitute the value of W (i.e. W = 9) into equation (1)
L = W + 3
L = 9 + 3
L = 12
Therefore, the length of the scrapbook is 12 in and the width is 9 in