Question 766574: An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 240 ft of picket fence are tobe used to enclose the garden, find the dimensions of the garden.
Answer by Shana-D77(132)   (Show Source):
You can put this solution on YOUR website! Though this question may feel horrible, it's a good one. Once you see how a question like this is answered, you'll be able to answer any similar question as they all follow the same pattern.
You have to create 2 equations from the given information. One of the equations we create will be based solely on the given information. To create the other, we'll need to remember either the area or perimeter formulas for a rectangle. We'll then be able to substitute the smaller equation into the other.
Our generic equations are:
A = lw
P = 2L + 2w
Now let's translate what we were given:
"width(w) IS (=) exactly two-thirds(2/3) of(multiply) the length(L)"
w = 2/3L
"240 ft of picket fence ARE (=) to be used to enclose (perimeter!) the garden"
240 = 2L + 2w
(we're not given anything related to area, which is good! Those become quadratics:)
Now to substitute...
If: 240=2L+2(w) and (w)=2/3L
**Then: 240 = 2L + 2(2/3L) **To find these problems easy in the future, this is the most important step to "get"**
Now solve...
240 = 2L + 4/3L (multiplied 2(2/3L))
240 = 10/3L (added 2L + 2/3L)
720 = 10L (multiplied both sides by 3)
72 = L (divided both sides by 10)
If the length is 72, let's find width:
240 = 2L + 2w
240 = 2(72) + 2w
240 = 144 + 2w
96 = 2w
w = 48
CHECK:
Does 48+48+72+72 = 240? yes!
Is 42 "exactly 2/3" of 72? (72*(2/3) = 48) yes!
Length = 72 feet
Width = 48 feet
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