The length of the rectangle is 5 times its width. Find the area of a rectangle if its perimeter is 156 cm.

1) Find the length and width of the rectangle. We are given a perimeter. The perimeter of a rectangle is the sum of the length and width of the rectangle multiplied by 2. Let’s write the formula:
P = (a + b) × 2,
where a is the length of the rectangle, b is the width.
In the statement of the problem it is said that the length of the rectangle is 5 times greater than the width, which means the width is 5 times less than the length, we write:
b = a / 5.
We substitute the value b in the formula for the perimeter of the rectangle and solve the equation with one unknown:
156 = (a + a / 5) × 2,
156 = 2a + 2a / 5,
156 = 10a / 5 + 2a / 5,
156 = (10a + 2a) / 5,
156 × 5 = 12a,
12a = 780,
a = 65.
This means that the length of the rectangle is 65 cm.Let’s find the width:
b = 65: 5 = 13 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,
where a is the length of the rectangle, b is the width.
S = 65 × 13 = 845 cm².
Answer: the area of ​​the rectangle is 845 cm².