SOLUTION: A rectangle has a length of 11 inches less than 3 times its width. If the area of the rectangle is 592 square inches, find the length of the rectangle. __inches

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Question 1134807: A rectangle has a length of 11 inches less than 3 times its width. If the area of the rectangle is 592
square inches, find the length of the rectangle.

__inches
Found 3 solutions by addingup, josgarithmetic, greenestamps:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
L x W = 592
(3W - 11) x W = 592
3W^2 - 11W = 592
3W^2 - 11W - 592 = 0
.
now factor the equation and you get:
3w2 - 48w + 37w - 592
Pull out common factors and add first two terms:
3w2 - 48w = 3W(W - 16)
now the last two terms:
37W - 592 = 37 x (w - 16)
put it all together:
(w - 16) x (3w + 37) = 0
w - 16 = 0
W = 16
or
3W + 37 = 0
3W = -37
W = -37/3
we are not looking for a negative number, so let's try 16:
16 x (3(16)-11) = 592
16 x (48 - 11) = 592
16 x 37 = 592 Correct, we have the correct answer

Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
Dimensions x and 3x-11;

.
.
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


You should of course know the method for solving this kind of problem using formal algebra.

But if an algebraic solution is not required, you can solve the problem much more quickly simply by finding two numbers with a product of 592 in which one number is 11 less than 3 times the other.
592 = 2*296
    = 4*148
    = 8*74
    = 16*37  <--  that one works: 37 = 3(16)-11

Done! The dimensions are 16 and 37
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