Is it possible to design a rectangular park

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

Ans:

Let’s consider the length of rectangular as X m and width as Y m.

By given 1^st condition, its perimeter is 80m

$\therefore 2(X + Y) = 80$

$\therefore X + Y = 40$

$\therefore X = 40 - Y$

By given 2^ndcondition, its area is 400 m²

$\therefore X Y = 400$ …. (ii)

By substituting value of X from equation (i) into equation (ii), we get:

$X Y = 400$

$\therefore (40 - Y) (Y) = 400$

$\therefore Y ^2 - 40 Y + 400 = 0$

$\therefore (Y - 20)^2 = 0$

$\therefore Y = 20$

By substituting value of X in equation (i), we get:

$X = 40 - Y$

$\therefore X = 40 - 20 = 20$

Therefore, the length of the rectangular park is 20 m and breadth is 20 m.

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