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

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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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Divya Prakash Singh

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