Find the dimensions of a rectangular park whose perimeter is 60 m and area 200 m2.

#Quadratic Equations
#Maths
#School
#CBSE 10 Class

Find the dimensions of a rectangular park whose perimeter is 60 m and area 200 m².

Answers (1)

Given $\rightarrow$ Perimeter of rectangle = 60 m
                Area of rectangle = 200 m
Let length be 'l' and breadth be 'b'
Accordig to question
            Perimeter $= 2\left ( l+b \right )= 60$
                            $\Rightarrow l+b= \frac{60}{2}= 30$
                           $\Rightarrow b= 30-l---(i)$
area $= l\times b= 200$
         $= l\times\left ( 30-l \right )= 200$    (from (i))
        $= 30l-l^{2}= 200$
        $= l^{2}- \left ( 20+10 \right )l+200= 0$
       $= l^{2}- 20l-10l+200= 0$
       $= l\left ( l-20 \right )-10\left ( l-20 \right )= 0$
       $= \left ( l-20 \right )\left ( l-20 \right )= 0\Rightarrow l= 10,20$
as $l> b ; hence\: l= 20$
$b= 30-20= 10\Rightarrow b= 10$      (from (i))
dimension of rectangle = $20\times 10$