SOLUTION: Hi, I am reviewing to retake the SAT's and need help with the following problem. If the perimeter of a rectangular property is 46 meters, and the area of the property i

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Question 623768: Hi,
I am reviewing to retake the SAT's and need help with the following problem.
If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 meters squared, what is the length of each of the shorter sides?
Knowing the steps to take would be very helpful.
Thanks!!
Found 2 solutions by jim_thompson5910, fcabanski:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
P = 2L + 2W

"If the perimeter of a rectangular property is 46 meters" ---> P = 46

46 = 2L + 2W

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Area = Length * Width

A = LW

"the area of the property is 76 meters squared" ----> A = 76

76 = LW

W = 76/L

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46 = 2L + 2W

46 = 2L + 2(76/L)

I'll let you finish up. Let me know if you have any questions or if you still need help. Thanks.

Answer by fcabanski(1391) (Show Source):
You can put this solution on YOUR website!
Is this multiple choice or write in? The strategy for each type of problem is different.

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.

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.

2L = 46-2W thus L = 23-W

(23-W)W = 76 thus and

Use the quadratic equation or the guess and check to find that quadratic factors to (W-19)(W-4) so W=19, 4.

L= 4 or L =19.

Since the question asks for the length of the shorter sides, the answer is 4.

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