Sierra planted a 12ft. by 10ft. flower garden in her backyard. She put a gravel walkway of uniform width around it. How wide was the walkway if she used 168ft^2 of gravel?

Answer 1

area including path - area inside path = area of path
area outside = (12+2w)(10+2w)
area inside = (12)(10) =120

so
path area = 120 +44w + 4 w^2 -120
= 4(w^2+11w) = 168 ft^2
w^2 + 11 w = 42
w^2 + 11 w - 42 = 0
3 and - 14
so w = 3 ft wide