Find the sides of the rectangle if its area is 75 cm2 and the perimeter is 36 cm.

To solve this problem, it is necessary to draw up a system of equations.

x is the length of the rectangle.

y is the width of the rectangle.

2 * (x + y) = 36.

x * y = 75.

x + y = 36/2 = 18.

x * y = 75.

Express the length of the rectangle from the first equation and substitute it into the second.

x = 18 – y.

y * (18 – y) = 75.

18 * y – y ^ 2 = 75.

y ^ 2 – 18 * y + 75 = 0.

D ^ 2 = (-18) ^ 2 – 4 * 1 * 75 = 324 – 300 = 24.

D = √24 = 4.9.

x = (18 + 4.9) / 2 = 11.45 cm.

y = 18 – 11.45 = 6.55 cm.

Answer:

Length 11.45 cm, width 6.55 cm.