# The area of the rectangle is 120 cm², while one of the sides is 14 cm larger than the other.

**The area of the rectangle is 120 cm², while one of the sides is 14 cm larger than the other. What are the sides of this rectangle?**

1. To calculate each of the sides, it is necessary to draw up an equation that will be an area formula with known parameters.

2. Recall the formula for finding the area of a rectangle:

S = a * b, where a and b are the sides of the rectangle.

3. We know that one side is 14 cm larger than the other, that is, b = a – 14.

4. Substitute in the area formula the side b, expressed in terms of a:

S = a * b = a * (a – 14).

5. Since we know the area, we get the equation:

a * (a – 14) = 120.

6. Let’s solve it:

a ^ 2 – 14a – 120 = 0;

D = b ^ 2 – 4ac = (-14) 2 – 4 · 1 · (-120) = 676;

a1 = (- (- 14) + √676) / (2 * 1) = 20;

a2 = (- (- 14) – √676) / (2 * 1) = -6;

Since we have a length, therefore the value a2 = -6 does not suit us.

7. We get that the sides are equal:

a = 20 (cm);

b = a – 14 = 20 – 14 = 6 (cm).

Answer: a = 20 (cm); h = 6 (cm).