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

Question

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

Sapling Academy · Accepted Answer

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

By given 1st condition, its perimeter is 80m

$	herefore 2(X + Y) = 80$

$	herefore X + Y = 40$

$	herefore X = 40 - Y$

By given 2nd condition, its area is 400 m2

$	herefore X Y = 400$ .... (ii)

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

$X Y = 400$

$	herefore (40 - Y) (Y) = 400$

$	herefore Y ^2 - 40 Y + 400 = 0$

$	herefore (Y - 20)^2 = 0$

$	herefore Y = 20$

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

$X = 40 -  Y$

$	herefore X = 40 - 20 = 20$

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

Please do press "Heart" button if you liked the solution.

Contact us