A rectangle and an equilateral

triangle have the same

perimeter.

The longest side of the

rectangle is 5cm longer than

the shortest side. The side of

the equilateral triangle is

double the shortest side of the

rectangle. Find the area of the

rectangle.

The area of the rectangle = 50 cm^2.

Step-by-step explanation:

Let the shortest side of the rectangle be x cm.

Perimeter of the rectangle is:

2x + 2 (x + 5).

Perimeter of the triangle = 3 * 2x.

As they have the same perimeter:

2x + 2 (x + 5) = 3*2x

2x + 2x + 10 = 6x

6x - 2x - 2x = 10

2x = 10

x = 5 cm.

So the area of the rectangle = x (x + 5)

= 5 * 10

= 50 cm^2.