The diagonal of the rectangle is 20 cm, and one side of the rectangle is 4 cm larger.

The diagonal of the rectangle is 20 cm, and one side of the rectangle is 4 cm larger. Find the sides of the rectangle using the equation.

1. Let’s denote one side of the rectangle by x.

Then the second side, according to the condition of the problem, is 4 cm larger, and therefore is equal to x + 4 cm.

2. The diagonal divides a rectangle into two triangles, its value can be calculated as the hypotenuse of a right-angled triangle according to the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the legs.

Let’s make the equation

d² = x² + (x + 4) ²;

400 = x² + x² + 8 x + 16;

2 x² + 8 x – 384 = 0;

x² + 4 x – 192 = 0, solve the quadratic equation and calculate only the positive value of the root

x = (-2 + √4 + 192);

x = (-2 + √196 = – 2 + 14 = 12 cm.

Answer: Diagonal = 12 cm.