# Find the sides of a rectangle if it is known that one of them is 17 cm larger than the other

**Find the sides of a rectangle if it is known that one of them is 17 cm larger than the other, and the diagonal of the rectangle is 25 cm.**

1. According to the problem statement, the diagonal of the rectangle is 25 cm, one side is 17 cm larger than the other.

2. Let’s designate the width as x cm, then the length will be equal to (x + 17) cm.

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs, for a given rectangle the equality is true:

x² + (x + 17) ² = 25², or x² + x² + 2 * 17 x + 289 = 625.

Let’s solve the quadratic equation:

2 x² + 34 x – 336 = 0, that is, x² + 17 x – 168 t = 0, whence

x = (-17 + √289 + 4 * 168): 2 = (-17 + √961): 2 = (-17 + 31): 2 = 14: 2 = 7 cm.

Let’s calculate the length:

7 cm + 17 cm = 24 cm.

Answer: The length is 24 cm, the width is 7 cm.