# I want to design a rectangular park whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as breadth of the rectangular park and altitude 12 m. Is it possible to have such a rectangular park? If so, find its length and breadth.

Let the length be area of rectangle= l(l – 3) = l2 – 3l

area of triangle= given

area of rectangle is 4sq mt more than triangle

so

area of rectangle – 4= area of triangle

l2 – 3l – 4 = 6l – 18

l2 – 9l + 14 = 0

l2 – 7l – 2l + 14 = 0

l(l – 7) – 2(l – 7) = 0

(l – 7)(l – 2) = 0

Yes, it is possible, to design a rectangular park.

L = 7 and 2

L = 2 is neglected as when length is 2 the breadth will be negative which is not possible...

so length= 7m

breadth= =7–3 = 4m

Yes it is possible to design a rectangular park having length & breadth 7 mts & 4 mts respectively.

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