Find the sides of a rectangle if its perimeter is 18 m and its area is 20 m ^ 2.

Given:

P = 18 m,

S = 20 m ^ 2,

a -?

b -?

Decision:

By determining the area and perimeter of a rectangle:

P = 2a + 2b (1)

S = a * b ——> a = S / b (2)

Substitute (2) in (1):

P = 2 * S / b + 2b = (2S + 2b ^ 2) / b;

Pb = 2S + 2b ^ 2;

2b ^ 2 – Pb + 2S = 0 (3)

Substitute the numerical values into the formula (3):

2b ^ 2 – 18b + 2 * 20 = 0; : 2

b ^ 2 – 9b + 20 = 0.

By Vieta’s theorem:

b1 = 4 (m);

b2 = 5 (m);

a1 = S / b1 = 20/4 = 5 (m);

a2 = S / b2 = 20/5 = 4 (m).

Answer: 4 m and 5 m or 5 m and 4 m.