Question

A rectangular garden plot must have a central planting area of length 13 m and width 8 m. there is to be a sidewalk around its perimeter with a width ww. if the total area, planting area plus sidewalk area, is 152 m22, what is the sidewalk width ww in meters?

Answer 1

(13+2w)*(8+2w)=152
104+26w+16w+4w²-152=0
4w²+42w-48=0

w=(−21+√633)/4≈1(m)

Answer 2

Width of the sidewalk is 1.04 m

Explanation:

A rectangular garden plot has a central planting area with dimensions 13m by 8m.

There is a sidewalk around the parameter with a width of w.

So the dimensions of the total area will be (13 + 2w)m by (8 + 2w)m.

Planting area plus sidewalk area is given as 152 m²

Now the total area = Length × width

152 = (13 + 2w) × (8 + 2w)

152 = 8(13 + 2w) + 2w(13 + 2w) [Distributive law]

152 = 104 + 16w + 26w + 4w²

152 = 4w² + 42w + 104

4w² + 42w + 104 - 152 = 0

4w² + 42w - 48 = 0

2w² + 21w - 24 = 0

w =
`\frac{-21\pm \sqrt{(21)^(2)-4(2)(-24)}}{2(2)}`

=
`(-21\pm √(441+192))/(4)`

=
`(-21\pm √(633))/(4)`

=
`(-21\pm 25.15)/(4)`

= 1.04 meters

Therefore, width of the sidewalk is 1.04 m