A vacant lot is being converted into a community garden.

Question

A vacant lot is being converted into a community garden. The garden and a walkway around its perimeter have an area of 754. Find the width of the walkway if the garden measures 12 feet wide by 15 feet long.

Answer 1

Let "x" be the width of the walkway. The total length is then 15 + x + x or 15 + 2x. And the total width is 12 + x + x or 12 + 2x. Since (for the total shape) Area = L_Total * W_Total and the Area is 754, then we can say:

L_Total * W_Total = 754 or

(15 + 2x)(12 + 2x) = 754

Multiplying this out gives us:

180 + 54x + 4x² = 754 or

4x² + 54x - 574 = 0 or (dividing by 2): 2x² + 27x - 287 = 0

Factoring, we get (x - 7)(2x + 41) = 0 and then (setting each piece equal to zero), x = 7 and x = -41/2

Since the walkway can't be a negative dimension, we can say the walkway is 7 feet wide.

Answer 2

754-180=574+4(corners)=578sq/ft.sidewalkarea1'width.

garden 12*15

574+4sq/ft

578+12=590

590+20

610+28

638+36

674+44

718+52

770-16=754

So 16/52=-.308/ft

I figure garden width=12+14-(14*.31)=21.69ft