A shed that measures feet by feet has a brick pathway of constant width built around it, so that the outer edge of the pathway is also a rectangle. The total area of the pathway is square feet. What is its width (in feet)?
Let x equal the width of the walkway.
The area of the whole thing is (2x + 8)(2x + 11) Why 2x? There's an x at each end of the
shed. Draw the picture and you'll see.
Multiply it out 4x2 + 38x + 88 (# 1)
The area of the shed alone is (8)(11) = 88 (# 2)
Subtract #2 from #1 4x2 + 38x This is the area of the walkway.
The problem says that the
area of the walkway is 120 so 4x2 + 38x = 120
Subtract 120 from both sides 4x2 + 38x – 120 = 0
Divide both sides by 2. This is
just to make it easier to factor. 2x2 + 19x – 60 = 0
Factor that (2x – 5)(x +12) = 0
So x = +5/2 and x = –12
A walkway can't have negative
width, so the walkway is 2.5 feet wide