Find the area of a rectangle if the perimeter is 58 and one side is 5 larger than the other.

Given:

ABCE – rectangle,

AB = 5 + BC centimeters,

the perimeter of ABCE is 58 centimeters.

Find the area of ​​the rectangle ABCE -?

Decision:

Consider the rectangle ABCE. Its opposite sides are equal to each other, then BC = AE, AB = CE.

Let the length of the BC side be x centimeters, then the length of the AB side = 5 + x centimeters. We know that the perimeter of AVSD is 58 centimeters. Let’s make the equation:

P avce = AB + CE + BC + AE;

58 = 5 + x + 5 + x + 5+ x + x;

4 * x = 58 – 10;

4 * x = 48;

x = 48: 4;

x = 12 centimeters – the lengths of the sides BC and AE;

12 + 5 = 17 centimeters – lengths of sides AB and CE;

S ABCE = 12 * 17 = 204 cm ^ 2.

Answer: 204 cm ^ 2.