SOLUTION: the length of a rectangle is four less than three times the width. the area is 160 square inches. find the perimeter

Question 247591: the length of a rectangle is four less than three times the width. the area is 160 square inches. find the perimeter
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
L = 3W - 4 (length is 4 less than 3 times the width)
.
L*W = 160 (area is given)
.
L = 160/W
.
Substituting in the first equation
160/W = 3W - 4
.
Multiply both sides by W
160 = 3W^2 -4W
.
Subtract 160 from both sides
0 = 3W^2 -4W -160
or
3W^2 - 4W - 160 = 0
.
Can we factor this? Yes.
(3W + 20)(W - 8) = 0
.
So our candidate values for W are: 8 and -6.667.
Since a negative number is nonsensical, we'll go with 8.
.
W = 8
.
Substituting back into our setup, we find L.
.
L = 160/W = 160/8 = 20
.
Always check your work!
.
A = L*W = 8 * 20 = 160
Is L = 3W - 4 true?
3W - 4 = 3(8) - 4 = 24 - 4 = 20
OK
...
But have we answered the question? Nope.
The question asked for the perimeter.
.
P = 2L + 2W
P = 2(20) + 2(8)
P = 40 + 16
P = 56
.
Now we're done.
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