Question

the perimeter of a rectangle is 24m and the area is 27 m sq. find its length and bredth. how to do this question?

Answer 1

Suppose l and b be the length and breadth of rectangle respectively.
So perimeter of rectangle = $2\left(l+b\right)$ = 24 i.e. $l+b=12...\left(i\right)$
Also area of rectangle = $lb=27$ i.e. $l=\frac{27}{b}$
Putting the value of l in (i) we get;
$$\begin{gathered} \frac{27}{b}+b=12 \\ \Rightarrow b^2+27=12b \\ \Rightarrow b^2-12b+27=0 \end{gathered}$$
Now splitting the middle term of this equation we get as;
$$\begin{gathered} b^2-9b-3b+27=0 \\ \Rightarrow b\left(b-9\right)-3\left(b-9\right)=0 \\ \Rightarrow \left(b-3\right)\left(b-9\right)=0 \\ \Rightarrow b=3;b=9 \end{gathered}$$
When $b=3$, then $l=\frac{27}{3}=9$
When $b=9$, then $l=\frac{27}{9}=3$
Since we always take longer side as length and smaller side as breadth,so we have;
Length = 9 cm and breadth = 3 cm