The perimeter of a rectangular flower garden is 60m and its area is 225 m^2. How do you find the length of the garden?

1 Answer
Mar 7, 2018

Length of the garden = 15m

Explanation:

Let l be the length (longer side) of the rectangular garden, and w be the width(shorter side).

Perimeter = 2(l+w) = 60m-----(1) given.
Area = lxxw= 225m^2------(2) given

(1) => 2l + 2w = 60

=> 2l = 60 - 2w

=> l = (60-2w)/2

Substitute l in (2):

=> w xx (60-2w)/2 = 225

=> 60w - 2w^2 = 225 xx 2

=> -2w^2 +60 w -550=0

=> 2w^2 - 60 w +550 =0

=> w^2 - 30w + 225 =0

Solving this quadratic equation:

=>w^2 - 15w -15w +225=0

=> w(w-15) -15(w-15) = 0

=> (w-15)(w-15) = 0

=> w -15=0

=> color(red)(w=15m)

So, the width is w=15m.

therefore (1) => 2(l+w) =60

=> 2(l +15)= 60

=> 2l +30 =60

=> l = 30/2= 15

color(red)(l= 15m)

That means the length of the rectangular garden is also 15m

This implies that the garden is color(red)(square) shaped with l= 15m and w=15m i.e. each Side = 15m