Find the perimeter of the rectangle, the length of which is 4 cm longer than its width and the area is 96 cm.

The area of a rectangle is the product of the sides of the shape.

Let’s write the first side of the rectangle as x.

Since the second is 4 cm larger, it will be equal to: x + 4 cm.

We get a quadratic equation:

x * (x + 4) = 96.

x ^ 2 + 4 * x – 96 = 0.

D ^ 2 = 16 – 4 * 1 * (-96) = 400.

D = 20.

x = (-4 + 20) / 2 = 16/2 = 8 cm (width).

x + 4 = 8 + 4 = 12 cm (length).

Find the perimeter of the rectangle.

To do this, we sum up all the sides of the figure with each other.

We get:

8 + 12 + 12 + 8 = 40 cm.

Answer:

Perimeter 40 cm.