Question

The ratio between the perimeter and the breadth of a rectangle is 5 ∶ 1. If the area of the rectangle is 216 sq. cm what is the length of the rectangle?

• A. 24 cm
• B. 18 cm
• C. 16 cm
• D. None of these

Answer 1

Answer:

B. 18 cm

Solution:

Given:

The ratio between the perimeter and the breadth of a rectangle = 5 : 1

The area of rectangle = 216 cm²

Formula used:

Area of rectangle = length × breadth

Perimeter of rectangle = 2(l + b)

Where, l = length and b = breadth

Calculation:

According to the question

$\frac{2(l+b)}{b}=\frac{5}{1}$

⇒ 2l + 2b = 5b

⇒ 2l = 3b

Now, area = 216 cm²

⇒ (l × b) = 216 cm²

⇒ $l\times{\frac{2l}{3}}=216cm^2$

⇒ l² = 324

⇒ l = 18 cm

∴ The length of the rectangle is 18 cm.