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

Answer:

Width of the sidewalk is 1.04 m

Step-by-step 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 = $\frac{-21\pm \sqrt{(21)^{2}-4(2)(-24)}}{2(2)}$

   = $\frac{-21\pm \sqrt{441+192}}{4}$

   = $\frac{-21\pm \sqrt{633}}{4}$

   = $\frac{-21\pm 25.15}{4}$

   = 1.04 meters

Therefore, width of the sidewalk is 1.04 m