The perimeter of the rectangle is 46 cm and its diagonal is 17 cm. What are the sides of the rectangle?

The perimeter of the rectangle is P = 46 cm, P = 2 * (a + b), 2 * (a + b) = 46, a + b = 23 cm (the sum of the sides of the rectangle).

The diagonal divides the rectangle into two right-angled triangles, then 17 ^ 2 = a ^ 2 + b ^ 2,

Then a = 23 – b,

17 ^ 2 = (23 – b) ^ 2 + b ^ 2;

289 = 529 – 2 * 23 * b + b ^ 2 + b ^ 2;

2 * b ^ 2 – 46 * b + 240 = 0;

b [1] = 15,

b [2] = 8;

a [1] = 8;

a [2] = 15.

The sides of the rectangle are 15 cm and 8 cm, or 8 cm and 15 cm.