The length of the diagonal of the rectangle is 17 cm, and the sum of its two non-parallel

The length of the diagonal of the rectangle is 17 cm, and the sum of its two non-parallel sides is 23 cm. Find the perimeter of the rectangle.

Let AB + BC = 23, AC = 17. ∆ABC – rectangular, by the Pythagorean theorem:

AB ^ 2 + BC ^ 2 = AC ^ 2. We denote AB = a, BC = b. We have a system of equations:

a + b = 23

a ^ 2 + b ^ 2 = 289.

Let us express a = 23 – b, substitute it into the second equation and solve it:

(23 – b) ^ 2 + b ^ 2 = 289;

2b ^ 2 – 46b + 240 = 0;

b2 – 23b + 120 = 0;

b1 = 8, b2 = 15.

a = 23 – b; a1 = 23 – 8 = 15; a2 = 23 – 15 = 8.

Take one set of numbers, let a = 8 cm, b = 15 cm, then the perimeter of the rectangle is:

P = 2 * (a + b) = 2 * (8 + 15) = 46 cm.

Answer: P = 46 cm.