The length of a rectangle is four times its width. If the perimeter of the rectangle is 100m , find its area.

Answer 1

This problem can be solved by creating an equation and solving it to find the dimensions of the rectangle.

Let's use the variable w to represent the width of the rectangle.

Then we can write the following expression to represent the length of the rectangle: 4w

Since the perimeter of a rectangle can be calculated by adding 2 times the length to 2 times the width , we can write the following equation for the perimeter (P) of the rectangle:

P = 2 • length + 2 • width

100 = 2 • (4w) + 2 • w

Now multiply, combine like terms, and use inverse operations to determine the value of w:

100 = 8w + 2w

100 = 10w

100/10 = 10w/10

10 = w

The width of the rectangle is 10 m .

The length will be 4 times the width or 4 • 10 = 40 m

Now that we know the length and the width of the rectangle , we can determine its area:

A = length • width

A = 40 • 10

A =400 m²