The length of the sides of the rectangle is expressed in centimeters and its perimeter is 16 cm

The length of the sides of the rectangle is expressed in centimeters and its perimeter is 16 cm and the area is 15 cm2. Find the sides of this rectangle.

Let the sides of the rectangle be a and b centimeters. Then the perimeter is

2 * a + 2 * b = 16 centimeters

Side b can be expressed in terms of a

2 * (a + b) = 16

a + b = 8

b = 8 – a

Since the area of the rectangle is 15 square centimeters, you can write the equation

a * (8 – a) = 15

8 * a – a * a = 15

a * a – 8 * a + 15 = 0

Since the square root of 4 * 4 – 15 is 1, the equation has two roots

a = 4 + 1 = 5 centimeters

a = 4 – 1 = 3 centimeters

Since the second side b = 8 – a, the sides of the rectangle are 3 and 5 centimeters