The diagonal of the rectangle is 10 cm and its perimeter is 28 cm, find the sides of the rectangle.

There is a rectangle for which the diagonal and perimeter values are known.

Find the sides of the rectangle.

Let’s introduce variables. Let a be the length of the rectangle and b its width.

The diagonal of a rectangle divides it into two equal right-angled triangles. In each of these triangles, the legs are the sides of the rectangle, and the hypotenuse is the diagonal. Let’s apply the Pythagorean theorem:

10 ^ 2 = a ^ 2 + b ^ 2.

P = 2 * (a + b);

a + b = 14.

b = 14 – a. Substitute the value b in the equation of the theorem:

a ^ 2 + (14 – a) ^ 2 = 100;

a ^ 2 + a ^ 2 – 28 * a + 196 = 100;

2 * a ^ 2 – 28 * a + 96 = 0;

a ^ 2 – 14 * a + 48 = 0;

a1 = 6;

a2 = 8.

The sides of the rectangle are 6 and 8 cm.