Question

A rectangular garden is fenced on three sides with a wall forming the fourth

The total length of the fence is 30 m. The area of the garden is 100 m². Find the
dimensions of the garden.​

Answer 1

The dimensions are 5 m by 20 m.

Explanation:

The area = length * width = 100 m^2.

2 times the width + the length = 30 m.

So we have the equations:

wL = 100

2w + L = 30

From the first equation:

L = 100/w so substituting in the second equation, we have:

2w + 100/w = 30

Multiply through by w:

2w^2 + 100 = 30w

2w^2 - 30w + 100 = 0 Divide by 2:

w^2 - 15w + 50 = 0

(w - 5)(w - 10) =

w = 5 or 10m.

So L = 100/5 or 100/10

= 20 or 10.

As it is rectangular then w = 5 and L = 20.