The area of the rectangle is 40 cm2, and its perimeter is 26 cm. What is the length and width of the rectangle?

1. Knowing that the area of a triangle is 40 cm², then the following equality is true:

S = a * b;

40 = a * b;

2. Knowing that the perimeter of the triangle is 26 cm, then the following equality is true:

P = 2 * (a + b);

26 = 2 * (a + b);

3. Let us express from the first equality a and substitute it into the second:

26 = 2 * (40 / b + b);

13 = 40 / b + b;

13 * b = 40 + b ^ 2;

b ^ 2 – 13 * b + 40 = 0;

We solve the quadratic equation:

D = 13 ^ 2 – 4 * 40 = 169 – 160 = 9;

x1 = (13 – 3) / 2 = 5;

x2 = (13 + 3) / 2 = 8;

Answer: the length and width of the rectangle are 5 and 8 cm.