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Question

A rectangular park is to be designed 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 the breadth of the rectangular park and of altitude 12 m. Find length and breadth of rectangular park.

Solution
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Here, Length of Rectangular Park =l

Breadth of Rectangular Park =l3

Altitude of Triangular Park =12

Breadth of Triangular Park =l3

Now,

ARectangle=l(l3)

ATriangle=12×12(l3)

ARectangleATriangle=4
l(l3)12×12(l3)=4
l29l+14=0
(l2)(l7)=0l=2,7


Since, breadth is l3 , l2

l=7 m and breadth =73=4 m

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