Question

Suzanne has a rectangular garden which is 18 feet long and 11 feet wide. She has 168 square foot of paving stones, and she wants to build a pathway around the border of the garden. How wide will the pathway be?

Answer 1

Answer:

width = 2.5 feet

Step-by-step explanation:

Suzanne has a rectangular garden which is 18 feet long and 11 feet wide.

Area of the garden = length times width = 18 times 11= 198 square foot

Let 'w' be the width of the border

Length of the garden with border = 18+2w

Width of the garden with border = 11+2w

Area of the garden with border = $(18+2w)(11+2w)=4w^2+58w+198$

Area of the border = $4w^2+58w+198-198=4w^2+58w$

She has 168 square foot of paving stones,

$4w^2+58w=168$

Solve for w

apply quadratic formula

a= 4, b= 58 and c=-168

$\quad x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$w=\frac{-58+-\sqrt{58^2-4\cdot \:4\left(-168\right)}}{2\cdot \:4}$

$w=\frac{-58+-\sqrt{6052}}{8}$

we get two values for w

$w=\frac{-58+\sqrt{6052}}{8}=2.47$

$w=\frac{-58-\sqrt{6052}}{8}=-16.97$