Question

Half the perimeter of a rectangular room is 46 m, and its length is 6 m more than its breadth. What is the length and breadth of the room?
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Answer 1

Let $l$ and $b$ be the length and breadth of the room respectively.
Then, the perimeter of the room is $2(l+b)$ metres.

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From the question,

$l=6+b$ ...(1)

$\frac{1}{2}\times 2(l+b)=46$

$\Rightarrow l+b=46$ ...(2)
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Let's solve these two equations using substitution method.

On substituting the value of $l$ from (1) in (2), we get

$6+b+b=46$

$\Rightarrow$ $6+2b=46$

$\Rightarrow 2b=40$

$\Rightarrow b=20m$

$\Rightarrow l=20+6=26m$

Therefore, length and breadth are 26 m and 20 m long respectively.
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