Question

A gravel path of equal width is to be built around a 10' by 10' square garden. How wide can the be if there is enough gravel for 224 2square ft?

Answer 1

The area for the path is equal to the area of the outside box minus the area of the inside box and is equal to 2242 sq ft.........Or is it 224 sq ft.??

Answer 2

it was supposed to be 224 square feet

Answer 3

We will get that strtaightened out later.

Path Area = (10+2x)(10+2x)=100+40x+4x^2=224
4x^2+40x-124=0 divide thru by 4
x^2+10x-31=0 Now use quadratic formula.

Answer 4

Wait a minute, I didn't subtract the inside box.
Path Area = (10+2x)(10+2x)-100=100+40x+4x^2-100=224

Answer 5

4x^2+40x-224=0 divide thru by 4
x^2+10x-56=0
(x+14)(x-4)=0
x=4
Looks like it will be 4 ft wide.

Answer 6

Since the other value is negative (-14) we should discard that root.

Answer 7

Did you have a value of 4 as an option?

Answer 8

Absolutely did. Thank you very much...quadratic equations always get me turned around.

Answer 9

Fortunately, when I correct the equation, we did not have to travel the quadratic path, just had to factor (thankfully)lol.