The length of the rectangle is 13 cm longer than its width. The area of the rectangle is 140cm. Find the perimeter of the rectangle.

Length (a) -? cm, 13 cm more than b;

Width (b) -? cm;

Area (Sp.) – 140 cm ^ 2;

Perimeter (Ppr.) -? cm.

First, we express the length of the rectangle in terms of its width:

a = b + 13 (cm).

It is known that the area of ​​the rectangle is equal to: Sppr. = a * b.

Thus, for a given rectangle it is true: a * b = 140, i.e .:

(b + 13) * b = 140;

b ^ 2 + 13b – 140 = 0;

D = (13) ^ 2 – 4 * 1 * (-140) = 169 + 560 = 729; sqrt (D) = 27;

x1 = (-13 + 27) / 2 = 7;

x2 = (-13 – 27) / 2 = -20 – the root is not suitable, because the width value cannot be negative.

So, the width of the given rectangle is b = 7 (cm).

Hence, its length is a = b + 13 = 7 + 13 = 20 (cm).

The perimeter of the rectangle is calculated using the formula:

Ppr. = (a + b) * 2 = (20 + 7) * 2 = 54 (cm).

Answer: The perimeter of the rectangle is 54 cm.