SOLUTION: A rectangular pool table has a perimeter of 14 m. If the area is 12 m2 find the dimensions.

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Question 1083210: A rectangular pool table has a perimeter of 14 m. If the area is 12 m2 find the dimensions.
Found 3 solutions by josgarithmetic, rothauserc, Alan3354:
Answer by josgarithmetic(39613) About Me  (Show Source):
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Dimensions x and y
system%28x%2By=7%2Cxy=12%29

You can check for two numbers whose sum is 7 and whose product is 12. They are 3 and 4.

Find the same using algebra if you want.
y=7-x and substitute.
-
x%287-x%29=12
7x-x%5E2-12=0
x%5E2-7x%2B12=0-----and this is factorable.

Answer by rothauserc(4718) About Me  (Show Source):
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We are given
:
Perimeter(P) = 14 = (2*l) + (2*w), where l is length and w is the width
Area(A) = l * w = 12
:
solve P equation for l
2l + 2w = 14
l + w = 7
l = 7 - w
:
substitute for l in the A equation
:
(7 - w) * w = 12
:
7w -w^2 = 12
:
w^2 -7w + 12 = 0
:
factor the quadratic
:
(w-4) * (w-3) = 0
:
we have two solutions
:
**********
w=4m, l=3m
w=3m, l=4m
**********
:

Answer by Alan3354(69443) About Me  (Show Source):
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Find a pair of factors of 12 with a sum of 7.