Question

The perimeter of a rectangle is equal to 138. The width of the rectangle is 5 less than the length . What is the area the rectangle?

Answer 1

Step 1: Concept

Perimeter of a rectangle = 2( L + W)

L = length

W = width

Area of a rectangle = Lenght x Width

Step 2:

Given data

The perimeter of a rectangle = 138

Length L = m

Width W = m - 5

Step 3:

`\begin{gathered} \text{Use the perimeter of the rectangle to find the length(L) and width(W).} \\ \text{Perimeter = 2(L + W)} \\ 138\text{ = 2(m + m - 5)} \\ 138\text{ = 2m + 2m - 10} \\ 138\text{ = 4m - 10} \\ \text{Collect similar terms} \\ 138\text{ + 10 = 4m} \\ 148\text{ = 4m} \\ m\text{ = }(148)/(4)\text{ = 37} \end{gathered}`

Step 4:

Length = 37

Width = 37 - 5 = 32

Step 5:

Find the area

Area = length x width

Area = 37 x 32

Area = 1184

Final answer

Area of the rectangle = 1184