Question

The area of a rectangular field is $120sqm.$. If the perimeter is $46m,$, find the length and breadth of the rectangle.

Answer 1

Let the length and breadth of rectangle be $xandy.$

So , perimeter $=2\times (x+y)$

$$\begin{gathered} 2\times (x+y)=46 \\ \Rightarrow x+y=\frac{46}{2} \\ \Rightarrow x+y=23 \\ \Rightarrow y=23-x------\left(1\right) \end{gathered}$$

Now, Area $=x\times y$

$$\begin{gathered} =x\times (23-x) \\ =23x-x^2 \end{gathered}$$

So,

$$\begin{gathered} 23x-x^2=120 \\ \Rightarrow x^2-23x+120=0 \\ \Rightarrow x^2-(15+8)x+120=0 \\ \Rightarrow x^2-15x-8x+120=0 \\ \Rightarrow x(x-15)-8(x-15)=0 \\ \Rightarrow (x-15)(x-8)=0 \\ either,x-15=0orx-8=0 \\ so,x=15orx=8 \end{gathered}$$

if

$$\begin{gathered} x=15 \\ then,y=23-15 \\ \Rightarrow y=8 \end{gathered}$$

So, length =$15m$and breadth =$8m$