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?

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?

radar · Answer

|dw:1335403726731:dw|

radar · Answer

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.??

anonymous · Answer

it was supposed to be 224 square feet

radar · Answer

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.

radar · Answer

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

radar · Answer

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.

radar · Answer

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

radar · Answer

Did you have a value of 4 as an option?

anonymous · Answer

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

radar · Answer

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