# 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.

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.

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