SOLUTION: I have a few problems and I just do not understand how to do them. It is not from a text book. Can you please help me? A rectangular garden has a dimension of 15 feet by 11 feet

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: I have a few problems and I just do not understand how to do them. It is not from a text book. Can you please help me? A rectangular garden has a dimension of 15 feet by 11 feet      Log On

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Question 186874: I have a few problems and I just do not understand how to do them. It is not from a text book. Can you please help me?
A rectangular garden has a dimension of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
given:
15%2A11+=+165 ft2 = The area of the garden
If the gravel path is of uniform width, it will
extend the width of the garden by 2x
and it will extend the length of the garden
by 2x also.
So, the area of garden + path =
%2815+%2B+2x%29%2A%2811+%2B+2x%29
Also I know area of garden + path =
165+%2B+192+=+357, so
%2815+%2B+2x%29%2A%2811+%2B+2x%29+=+357
165+%2B+22x+%2B+30x+%2B+4x%5E2+=+357
Subtract 165 from both sides
22x+%2B+30x+%2B+4x%5E2+=+192
Rewrite the left side
4x%5E2+%2B+52x+=+192
Divide both sides by 4
x%5E2+%2B+13x+=+48
x%5E2+%2B+13x+-+48+=+0
Use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+13
c+=+-48
x+=+%28-13+%2B-+sqrt%28+13%5E2-4%2A1%2A%28-48%29+%29%29%2F%282%2A1%29+
x+=+%28-13+%2B-+sqrt%28+169+%2B+192+%29%29%2F2+
x+=+%28-13+%2B-+sqrt%28+361+%29%29%2F2+
x+=+%28-13+%2B-+19%29%2F2+
x+=+3
x+=+-16 (not useful here)
The path can be 3 feet wide
check answer:
%2815+%2B+2x%29%2A%2811+%2B+2x%29+=+357
%2815+%2B+2%2A3%29%2A%2811+%2B+2%2A3%29+=+357
%2815+%2B+6%29%2A%2811+%2B+6%29+=+357
21%2A17+=+357
357+=+357
OK