A rectangular plot of ground having dimensions 24 feet by 26 feet is surrounded by a walk of uniform width. If the area of the walk is 104 feet squared, what is its width?
2 answers
Boring
True, but that gets 0 points.
If the walk is w feet wide, then the inside dimensions are 24x26 and the outer dimensions are 24+w and 26+w. So, the area of the walk is the outer area minus the inner area.
(26+2w)(24+2w) - 26*24 = 624 + 100w + 4w^2 - 624 = 104
4w^2 + 100w - 104 = 0
w^2 + 25w + -26 = 0
(w-1)(w+26) = 0
So, w = 1 (-26 makes no physical sense)
26*28 - 26*24 = 26*4 = 104 as wanted.
If the walk is w feet wide, then the inside dimensions are 24x26 and the outer dimensions are 24+w and 26+w. So, the area of the walk is the outer area minus the inner area.
(26+2w)(24+2w) - 26*24 = 624 + 100w + 4w^2 - 624 = 104
4w^2 + 100w - 104 = 0
w^2 + 25w + -26 = 0
(w-1)(w+26) = 0
So, w = 1 (-26 makes no physical sense)
26*28 - 26*24 = 26*4 = 104 as wanted.
1 answer