SOLUTION: If there is a plot of land that is 24 by 30. And surrounding the land is a walkway that has an area of 247 ft. sq. what is the width of the walkway.

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Question 157797: If there is a plot of land that is 24 by 30. And surrounding the land is a walkway that has an area of 247 ft. sq. what is the width of the walkway.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
To understand this problem you should sketch/draw a 24 by 30 rectangle.
Then draw a larger rectangle on the outside of this rectangle representing the walkway.
Now assign the value x to the width of the sidewalk.
You now have a rectangle with dimensions of (24+2x) & (30+2x)
Calculate the area of the inner rectangle (the plot)+& add the additional 247 ft^2 & solve the equation.
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24*30=720 ft^2 for the plot.
(24+2x)(30+2x)=720+247
720+60x+48x+4x^2=967
4x^2+108x+720-967=0
4x^2+108x-247=0
Using the quadratic equation:x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+we get:
x=(-108+-sqrt[108^2-4*4*-247])/2*4
x=(-108+-sqrt[11,664+3,952]) /8
x=(-108+-sqrt15,616)/8
x=(-109+-124.964)/8
x=(-108+124.964)/8
x=16.964/8
x=2.12 feet is the width of the walkway.
Proof:
(24+2*2.12)(30+2*2.12)=967
(24+4.24)(30+4.24)=967
28.24*34.24=967
967=967