Word Problem

Question

a vacant lot is being turned into a community garden. the garden and the walkway around its perimeter have an area of 378 square feet. find the width of the walkway if the garden is 12ft wide by 15 feet long

Answer 1

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The walkway goes all around the perimeter of a garden that's 12 x 15 ft. So the area of the garden is 180 ft².

 

Now if you account for the walkway, the total area is 378 ft². So the walkway's area is 198 ft².

 

We'll assume that walkway has the same width all the way around, and we'll call it w.

 

The walkway has two pieces along the long sides of the garden, each with area 15w.

 

And it has two pieces along the short sides of the garden, each with area (12 - 2w)w. We have to make sure the corners aren't counted twice, and that's why I have to take off the a piece that's w in LENGTH at either end.

 

Add the four sides' areas together and set the total to 198.

 

2w(12 - 2w) + 2(15w)

= 54w - 2w² = 198

 

So

2w² - 54w + 198 = 0

or

w² - 27w + 99 = 0

 

w = (27 ± 3√37)/2

 

The answer that makes sense is the one with the minus sign. So w = about 4.4 ft.

 

Cheers!