Question 347821: A rectangular plot of ground having dimensions 25 feet by 38 feet is surrounded by a walk of uniform width. If the area of the walk is 568 ft 2 , what is its width?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular plot of ground having dimensions 25 feet by 38 feet is surrounded by a walk of uniform width.
If the area of the walk is 568 ft 2, what is its width?
:
Find the area of the plot of ground 25 * 38 = 950 sq/ft
;
Let w = the width of the walk
then
the overall dimensions will be: 2w+25 by 2w+38
then
(2w+25)*(2w+38) = total area of plot and walkway
FOILs to 4w^2 + 76w + 50w + 980 = 4w^2 + 126w + 980
:
overall area - plot area = walkway area
4w^2 + 126w + 950 - 950 = 568
4w^2 + 126w - 568 = 0
simplify, divide by 2
2w^2 + 63w - 284 = 0
You can use the quadratic formula, but this will factor
(2W + 71)(w - 4) = 0
the positive solution
w = 4 ft is the width of the walkway
:
:
See if that is true
Overall area: (8+25)*(8+38) = 1518
1518 - 950 = 568
Plot area: 980
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