1. A man has 22 feet by 26 feet rectangular lot that he will use for planting. He wants to build a brick of walkway of uniform width on the border of the lot. If the man wants to have 396 square feet of ground left for planting, how wide should he build the walkway?

Question

1.  A man has 22 feet by 26 feet rectangular lot that he will use for planting. He wants to build a brick of walkway of uniform width on the border of the lot. If the man wants to have 396 square feet of ground left for planting, how wide should he build the walkway?

2.  Based from Problem 1.  The man buys enough brick to build 160 square feet of walkway. Is this sufficient to build the walkway mentioned in Problem 1? If not, how wide can she build he walkway with these bricks?

3.  Refer to Problem 1. The man has 50 feet of fencing that he will use to enclose an area for flowering plants. Find the dimensions of the largest area he can fence. Find the largest possible rectangular area he can enclose.

Steve · Answer

(22-2w)(26-2w) = 396
w = 2

24*26-396 = 228
No, not enough brick
22*26 - (22-2w)(26-2w) = 160
w = 1.8

Not sure how #3 relates to #1
as with all such problems, divide the fencing evenly between the lengths and the widths. That means that a square 50/4 feet on a side will provide the maximum area. To see this, note that if the area has dimensions x and y,
2x+2y = 50
y = 25-x
The area is x*y = x(25-x) = 25x-x^2
This is just a parabola with vertex at x=25/2, as described above.