Question

A rectangles perimeter and its area have the same numerical value. The width of the rectangle is 10. What is the length of the rectangle? (Answer as a decimal.)

Answer 1

Answer:

The length of the rectangle, L = 2.5 units

Step-by-step explanation:

Given the following data;

Length of rectangle =?

Width of rectangle = 10 units.

Note:

The formula for calculating the perimeter of a rectangle is;

$P = 2L + 2W$  ........equation 1

Substituting into equation 1, we have;

P = 2L + 2(10)

P = 2L + 20

The formula for calculating the area of a rectangle is given by;

$A = L * W$ ..........equation 2

Substituting into equation 2, we have;

A = 10L

Since, the perimeter of the rectangle is equal to its area;

Perimeter = Area

2L + 20 = 10L

20 = 8L

L = 20/8

L = 2.5 units.