Question 623768
Is this multiple choice or write in?  The strategy for each type of problem is different. <P>
If multiple choice and if the answers are numbers, then plug in answers and see which work.  Remember the formula for area of a rectangle is LW=A and for Perimeter is 2L + 2W = P.<P>
If it's not multiple choice then solve the second equation for L in terms of W, plug it into the first equation, and solve for W.<P>
2L = 46-2W thus L = 23-W<P>
(23-W)W = 76 thus {{{23W - W^2 = 76}}} and {{{W^2-23W+76=0}}}<P>
Use the quadratic equation or the guess and check to find that quadratic factors to (W-19)(W-4) so W=19, 4.<P>
L= 4 or L =19.<P>
Since the question asks for the length of the shorter sides, the answer is 4.<P>
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