If the perimeter of a rectangle is 75 meters, and the length is 1.5 times the width, find the area of the rectangle in square meters. round your answer to the two decimal points.

937.50 square meters
8.66 square meters
225.00 square meters
527.34 square meters
337.50 square meters

E. The area of the rectangle is 337.5 square metres

Step-by-step explanation:

Given

Shape: Rectangle

Perimeter = 75 m

Length = 1.5 * Width

Required:

Area of the rectangle

First, the value of the length and the width of the rectangle need to be calculated.

Let L and W represent the length and width of the rectangle, respectively.

Hence,

Length = 1.5 * Width can be represented by

L = 1.5 * W

L = 1.5W

Also, let P and A represent the perimeter and area of the rectangle.

Using the formula of perimeter; we have

P = 2(L + W)

By substituting 1.5W for L and 75 for P, the equation becomes

75 = 2(1.5W + W)

75 = 2(2.5W)

Open bracket

75 = 5W

Divide through by 5

15 = W.

Recall that L = 1.5W

So, L = 1.5 * 15

L = 22.5

Since L and W represent the length width of the rectangle,

Then

Length = 22.5m and Width = 15m

Area of a rectangle is calculated by multiplying its length by its width.

So,

Area = 22.5m * 15m

Area = 337.5 m²

Hence, the area of the rectangle is 337.5 square metres