The perimeter of the rectangle is 52 cm, the width is 6 cm shorter than the length, find the area of the rectangle.

The perimeter of a rectangle is the sum of the length and width of the rectangle multiplied by 2.

* 1) Find the length and width of the rectangle. Let’s denote the length of the rectangle by the letter a, and the width by the letter b.

According to the condition of the problem, the width is shorter than the length of the rectangle by 6 cm.

Let’s express the width of the rectangle in terms of the length:

b = a – 6.

Let’s write an expression for calculating the perimeter of a rectangle:

P = (a + b) × 2.

Substituting the value of the perimeter into the formula, and instead of the width b, the resulting expression, we solve the equation with one unknown a:

52 = (a + (a – 6)) × 2;

52 = (a + a – 6) × 2;

52 = (2a – 6) × 2;

52 = 4a – 12;

4a = 52 + 12;

4a = 64;

a = 16 cm.

b = 16 – 6 = 10 cm.

* 2) Find the area of ​​the rectangle.

The area of ​​a rectangle is the product of the lengths of its sides. Let’s write the formula for the area:

S = a × b,

S = 16 × 10 = 160 cm².

Answer: the area of ​​the rectangle is 160 cm².