First step: Draw a picture, so you can see what you are trying to solve.
Length = X
_________________
| | |
| | | Width = W
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granted, this is a poor drawing, but i trust you are able to understand that this is a rectangle divided in the middle.
Let's label one side W (Choose any side, but in this case, I choose the shortest side.)
What numbers does the problem give?
What ratios does the problem give?
What do these numbers mean?
36 feet total of fencing
W (width) is 1/3 length of L (length)
As a 2-step problem.....
You can see by the picture that there are two sides the divider which all have length W.
You can see there are two sides (top and bottom) which measure length L
If you add them all you get the total of 36 ft.
3W + 2L = 36
W is 1/3 L (Remember that IS/ARE always means = )
W = 1/3 L which is the same as 1L/3)
as a two step problem, substitute :
3(L/3) + 2L = 36 then, simplify.
L +2L = 36
3L = 36 divide both sides by 3
3/3 L = 36/3
L = 12 ( the top is length 12, but you still have to find the width; W)
W = L/3
W = 12/3 = 4
report both answers: L = 12, W = 4
second option;
Label the SIDE width as X.
Since the length X = 1/3 TOP, multiply both sides by 3
TOP = 3X ( and TOP = BOTTOM)
now your equation is:
top + bottom + 3 sides = 36
3X + 3X + 3X = 36 simplify
9X = 36 divide both sides by 9
x = 4 ( you have found the width, now you can easily find the top (length))
TOP = 3X = 3 * 4 = 12
always report both solutions;
W = 4, L = 12
