One of the diagonals of the rectangle is 17 and one of the sides is 8. Find the perimeter of the rectangle.

The diagonal of a rectangle is the hypotenuse of a right-angled triangle, the legs of which are the sides of the rectangle. By the Pythagorean theorem, we find the unknown side of the rectangle:

a ^ 2 + b ^ 2 = c ^ 2;

a ^ 2 + 8 ^ 2 = 17 ^ 2;

a ^ 2 = 17 ^ 2 – 8 ^ 2;

a ^ 2 = 289 – 64;

a ^ 2 = 225;

a = √225;

a = 15.

Find the perimeter of a rectangle with sides 8 and 15:

P = 2 * (a + b);

P = 2 * (15 + 8);

P = 2 * 23;

P = 46.

Answer: P = 46.