SOLUTION: A rectangular billboard sign has a length that is four yards longer than twice its width, x If the area of the sign is 30 square yards, which equation could be used to find the dim

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Question 1160885: A rectangular billboard sign has a length that is four yards longer than twice its width, x If the area of the sign is 30 square yards, which equation could be used to find the dimensions in yards of the sign?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A rectangular billboard sign has a length that is four yards longer than twice its width, x If the area of the sign is 30 square yards, which equation could be used to find the dimensions in yards of the sign?
if a billboard sign length is 4yd longer than twice its width we have
L=2W%2B4yd .........eq.1
if its area is 30yd%5E2, we have
L%2AW=30yd%5E2........eq.2
substitute L from eq.1 in eq.2
%282W%2B4yd%29%2AW=30yd%5E2............solve for W
2W%5E2%2B4yd%2AW=30yd%5E2
2W%5E2%2B4yd%2AW-30yd%5E2=0...simplify, divide by 2
W%5E2%2B2yd%2AW-15yd%5E2=0........ factor completely
W%5E2-3yd%2AW%2B5yd%2AW-15yd%5E2=0
%28%28W%5E2-3yd%2AW%29%2B%285yd%2AW-15yd%5E2%29%29=0
W%28W-3yd%29%2B5yd%28W-3yd%29=0
%28W+-+3yd%29+%28W+%2B+5yd%29+=+0+=+0

=> %28W+-+3yd%29+=+0->W+=+3yd
=> %28W+%2B5yd%29+=+0->W+=+-5yd->disregard negative solution


go to L=2W%2B4yd .........eq.1, substitute W

L=2%2A3yd%2B4yd
L=10yd

so, the dimensions of the rectangular billboard sign are:
the length: 10yd
the width: 3yd

Answer by ikleyn(52867) About Me  (Show Source):
You can put this solution on YOUR website!
.

    W*(2W+4) = 30  square yards (the area).


    W*(W+2)  = 15.


So, 15 is presented as the product of two factors that differ by 2.


Hence, guessing mentally,  W = 3;  W + 2 = 5.


    Or you can solve the equation (1) formally.


ANSWER.  W = 3 yards;  L = 2W + 4 = 2*3+4 = 10 yards.

Solved.