Answer:
From the information given,
Area of rectangle = 36 cm^2
length of rectangle is 5 cm longer than its width
We want to find the length and width of the rectangle
Let W represent the width of the rectangle. It means that
length of rectangle = W + 5
Recall,
Area = length x width
Thus,
W(W + 5) = 36
W^2 + 5W = 36
W^2 + 5W - 36 = 0
This is a quadratic equation. We would solve by applying the method of factorization. The first step is to multiply W^2 with - 36. It becomes – 36W^2. We would find two terms such that their sum or difference is 5W and their product is – 36W^2. The terms are 9W and - 4W By replacing 5W with 9W - 4W, we have
W^2 + 9W - 4W - 36 = 0
Factorize by grouping. It becomes
W(W + 9) - 4(W + 9) = 0
Since W + 9 is common, it becomes
(W + 9)(W - 4) = 0
W + 9 = 0 or W - 4 = 0
W = - 9 or W = 4
Since the width cannot be negative,
W = 4
length = 4 + 5 = 9
Thus, the dimensions are
length = 9 cm
width = 4 cm
Explanation:
The length is a single value
so is the width.
The length cannot be written as a multiplication of two numbers