Q5.    Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.

Answers (1)
D Divya Prakash Singh

Let us assume the length and breadth of the park be 'l'\ and\ 'b' respectively.

Then, the perimeter will be P = 2(l+b) = 80

\Rightarrow l+b = 40\ or\ b = 40 - l

The area of the park is:

Area = l\times b = l(40-l) = 40l - l^2

Given : 40l - l^2 = 400

l^2 - 40l +400 = 0

Comparing to get the values of a, b and c.

The value of the discriminant D = b^2-4ac

\Rightarrow = b^2-4ac = (-40)^2 - 4(1)(400) = 1600 -1600 = 0

As D = 0.

Therefore, this equation will have two equal roots.

And hence the roots will be:

l =\frac{-b}{2a}

l =\frac{-40}{2(1)} = \frac{40}{2} =20

Therefore, the length of the park, l =20\ m

and breadth of the park b = 40-l = 40 -20 = 20\ m.

 

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