The diagonal of the rectangle is 26 cm and its perimeter is 68 cm. Find the sides of the triangle.

The perimeter and diagonal of the rectangle are known. Let’s find its sides.

Let’s enter the variables right away. Let a be one side of the rectangle and b the second side. Based on the conditions of the problem, we will compose and solve a system of two equations with two unknowns.

2 * (a + b) = 68;

a ^ 2 + b ^ 2 = 676;

a + b = 34;

b = 34 – a;

Substitute b into the second equation:

a ^ 2 + (34 – a) ^ 2 = 676;

a ^ 2 + a ^ 2 – 68 * a + 1156 – 676 = 0;

2 * a ^ 2 – 68 * a + 480 = 0;

a ^ 2 – 34 * a + 240 = 0;

a = 10;

a = 24.

We got two side values – they will exactly be the side of the rectangle.