SOLUTION: A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of 425 square feet. How

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of 425 square feet. How       Log On


   

Question 265882: A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of 425 square feet. How wide will the walk be? Please show step-by-step work (full work) to make understanding how to solve the problem easier.
Answer by JBarnum(2146) About Me  (Show Source):
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A rectangular lawn is 24 feet wide by 32 feet long. A sidewalk will be built along the inside edges of all four sides. The remaining lawn will have an area of 425 square feet. How wide will the walk be? Please show step-by-step work (full work) to make understanding how to solve the problem easier.
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this will be hard to explain on here as i dont know how to draw the diagram u need to see to understand whats going on if u leave a comment i could scan an image with full work details to your email.
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but i will try below:
BIG Rectangle is "R" little rectangle is "r"
the Area of R=32(24)so R's Area is 768
the Area of r=a(b) r=425 is given
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("b" is the long side of "r", in the drawing you draw a rectangle in the middle of a bigger rectangle, put "b" for the long side of "r", "a" for the short side of "r",put 32 for the long side of "R",24 for the short side of "R". Also label "x" as the width of the sidewalk on both sides of line "b")
with the drawing you can see that 2x%2Bb=32.
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so if there is an equally consistant width(x) of the sidwalk that goes around "r" from "R" then the following is true:
32 is to "b" as 768 is to 425 => %2832%2Fb%29=%28768%2F425%29 cross multiply to find b
32%28425%29=768b

425=24b
425%2F24=b
use the equation from the drawing
2x%2Bb=32
2x%2B%28425%2F24%29=32
2x%2824%29%2B%28425%2Fcross%2824%29%29cross%2824%29=32%2824%29
48x%2B425=768
48x=343
x=343%2F48
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So the width of the side walk is exactly 343/48 or approx 7.1458333333333
check:
x+x+b=32
343%2F48%2B343%2F48%2B850%2F48=32
1536%2F48=32
32=32