Question 1161814: You have a vacant lot at your house backyard. You want yourself to be productive every weekend. You decided to make a vegetable garden. You want it that its length of the plot is equal to triple the width.
Questions:
1. Which system of equations can be used to find the dimensions of the plot if you want it to have a perimeter of 32 feet?
2. If your backyard measures 12 x 12 feet, how many garden plot/s can you make? Why?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the length and y equal the width.
the area of the plot is x * y
the perimeter of the plot is 2x + 2y, or: 2 * (x + y)
if you want the length of the plot to be equal to triple the width, then set x = 3y
the area of the plot becomes 3y * y = 3y^2.
the perimeter of the plot becomes 2 * (3y + y) = 2 * 4y = 8y
if you want the perimeter of the plot to be equal to 32 feet, then your two equations would be:
2 * (x + y) = 32
x = 3y
replace x in the first equation with 3y to get:
2 * (3y + y) = 32
simplify to get 8y = 32
solve for y to get y = 4
solve for x to get x = 3*4 = 12
the dimensions of the plot would have a length of 12 and a width of 4.
the perimeter of the plot would be 2 * (12 + 4) = 2 * 16 = 32.
the backyard measures 12 by 12.
since the length of your plot is 12 and the width of your plot is 4, then you can get 3 plots of (4 by 12) each in the 12 by 12 back yard.
they would be layed out something like this:
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