Question

The length of a rectangle is 4 more than two times the width. The minimum perimeter is 80. Determine the minimum length of the rectangle that can satisfy the condition.

• A. 28
• B. 12
• C. 30
• D. 32

Answer 1

The correct option is A 28

Let, Width of a rectangle $=x$
Given, The length of a rectangle is 4 more than two times the width.
So, Length = 4 + 2x

As we know,
Perimeter of a rectangle = 2(Length + breadth) $=2(4+2x+x)$
Perimeter of a rectangle $\ge 40$
$2(4+2x+x)\ge 80$
Transfer 2 to the R.H.S
$4+3x\ge \frac{80}{2}$
$4+3x\ge 40$ ($\because \frac{80}{2}=40,2x+x=3x$)
Subtract 4 from both the sides
$4-4+3x\ge 40-4$
$3x\ge 36$
Transfer 3 to the R.H.S
$x\ge \frac{36}{3}$
$x\ge 12$
Length $=4+2x$
Therefore, Length $\ge 4+2\left(12\right)$ (Since $x\ge 12$)
Length of a rectangle $\ge 28$
A closed circle at $28$ and the red line goes to the left, indicating that $x$ is greater than or equal to $28$

Hence, option (a.) is the correct choice.