Question

The perimeter of a rectangular garden is 100 feet​ (ft). the area of the rectangular garden area is 600 ft2. find the length and width of the garden. let the length of the garden be the shorter​ side, of necessary.

Answer 1

let the length be x and the width be y:
Area=x*y=600
thus
x=600/y

Perimeter=2(L+W)
100=2(x+y)
substituting the value of x we obtain:
100=2(600/y+y)
solving for y we shall have:
50=600/y+y
50y=600+y^2
thus
y^2-50y+600=0
solving the quadratic we obtain:
y=20 or y=30
thus the length=30 ft and the width=20 ft