Find the area of a rectangle, one of the diagonals of which is 13 cm and the sum of two adjacent sides of the wound is 17 cm.

In order to find the area of ​​a rectangle, if it is known that one of its diagonals is 13 cm, and the sum of two adjacent sides of the wound is 17 cm, we will apply the formula to calculate the area:

S = a * b;

We denote by x cm the length of one of the sides, then the length of the second side is (17 – x) cm.

Consider a right-angled triangle formed by the sides of a rectangle (legs) and a diagonal (hypotenuse).

Let’s apply the Pythagorean theorem:

13 ^ 2 = x ^ 2 + (17 – x) ^ 2;

x ^ 2 + x ^ 2 – 34x + 289 = 169;

2x ^ 2 – 34x + 120 = 0;

x ^ 2 – 17x + 60 = 0;

D = 289-240 = 49;

x1 = (17 – 7) / 2 = 5;

x2 = (17 + 7) / 2 = 12.

5 and 12 cm sides of the rectangle.

S = 5 * 12 = 60 sq. cm.