# Find the sides of the rectangle if you know that one of them is 14 cm larger than the other

**Find the sides of the rectangle if you know that one of them is 14 cm larger than the other, and the diagonal of the rectangle is 34 cm.**

Since the diagonal of the rectangle divides it into two equal right-angled triangles, the sides of the rectangle will be the legs of this triangle, and the diagonal will be its hypotenuse.

Using the Pythagorean theorem, we compose an equation, where x is one of the sides of the rectangle, and x + 14 is its other side:

x ^ 2 + (x + 14) ^ 2 = 34 ^ 2;

x ^ 2 + x ^ 2 + 28x + 196 = 1156;

2x ^ 2 + 28x – 960 = 0.

Reduce the equation by 2:

x ^ 2 + 14x – 480 = 0.

The root of the discriminant is 46.

x1 = (-14 – 46) / 2 = -30 is a negative number, therefore it is not suitable for solving the problem;

x2 = (-14 + 46) / 2 = 16 cm – the length of one of the sides of the rectangle;

16 + 14 = 30 cm – the length of the other side of the rectangle.

Answer: 16 cm, 30 cm.