Question

A rectangular room has a length of $x$ m and breadth of ($x+2$) m. The length of rope used to measure the length and breadth of a room is less than 24 m. Calculate the maximum length of the room if $x$ is in positive integers.

• A. 4 m
• B. 6 m
• C. 8 m
• D. 2 m

Answer 1

The correct option is A 4 m

Concept: Perimeter of the room = length of the rope
Given,
Length of the room $=xm$
Breadth of the room $=x+2m$
Length of the rope = Perimeter of the room < 24 m

As we know,
$\to$ Perimeter of the room = 2( length + breadth)
$\Rightarrow 2(x+(x+2\left)\right)<24$
$\Rightarrow 2(2x+2))<24$

Divide by 2 on both sides of the inequality,
$\Rightarrow \frac{2(2x+2))}{2}<\frac{24}{2}$
$\Rightarrow 2x+2<12$

Subtract 2 from both sides of the inequality,
$\Rightarrow 2x+2-2<12-2$
$\Rightarrow 2x<10$
$\Rightarrow 2x<10$

Divide by 2 on both sides of the inequality
$\Rightarrow \frac{2x}{2}<\frac{10}{2}$
$\Rightarrow x<5$

As $x$ is in positive integers and value of $x$ is less than 5, hence
values of $x$: 4, 3, 2, 1
A opened circle at $5$ and the red line goes to the left, indicating that $x$ is less than $5.$



Maximum value of $x$ = 4
Hence, maximum lnegth of the room = 4 m