One side of the rectangle is 4 cm larger than the other side, and the area is 60 cm2.

One side of the rectangle is 4 cm larger than the other side, and the area is 60 cm2. Find the lengths of the sides of the rectangle.

Because the sides of the rectangle are unknown, but the area of ​​the rectangle is known, we denote the length of the rectangle as x cm, then the width of the rectangle will be (x + 4) cm.In order to find the area of ​​the rectangle, the length of the rectangle must be multiplied by its width. Let’s make the equation:

x * (x + 4) = 60;

x ^ 2 + 4x = 60;

x ^ 2 + 4x – 60 = 0;

Find the discriminant of the quadratic equation:

D = b ^ 2 – 4ac = 4 ^ 2 – 4 1 (-60) = 16 + 240 = 256

Since the discriminant is greater than zero, the quadratic equation has two real roots:

x1 = (-4 – √256) / 2 * 1 = (-4 – 16) / 2 = -20 / 2 = -10;
x2 = (-4 + √256) / 2 * 1 = (-4 + 16) / 2 = 12/2 = 6.

The length cannot be negative, so the length of the rectangle is 6 cm, then the width is 6 + 4 = 10 cm.

Answer: 6 cm and 10 cm.