Question

Is it possible to design a rectangular park of perimeter $80$ m and area $400$ m${}^2$ ? If so, find its length and breadth.

• A. Length $=$ $40$m breadth $=$ $10$ m
• B. Length $=$ $60$m breadth $=$ $30$ m
• C. Length $=$ breadth $=$ $50$ m
• D. Length $=$ breadth $=$ $20$ m

Answer 1

Answer: (D)

Length $=$ breadth $=$ $20$ m

Let the length of the park be $x$ m
Hence, breadth will be $(40-x)$ m
Therefore, area will be $\left(x\right)(40-x)=400$
$40x-x^2=400$
$x^2-40x+400=0$
$(x-20{)}^2=0$
$x=20$ m
Hence, length = $20$ m and breadth= $40-20=20$ m