SOLUTION: if a rectangle has an area of 117cm2 and a perimeter of 44cm what is it's length and breadth

Question 240431: if a rectangle has an area of 117cm2 and a perimeter of 44cm what is it's length and breadth
Found 2 solutions by stanbon, checkley77:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
if a rectangle has an area of 117cm2 and a perimeter of 44cm what is it's length and breadth
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width = x
length = y
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Area = xy = 117 cm^2
Perim = 2(x+y) = 44 cm
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x+y = 22
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Solve for y:
y = 22-x
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Substitute into xy = 117 and solve for "x":
x(22-x) = 117
-x^2 + 22x - 117 = 0
x^2 - 22x + 117 = 0
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Quadratic formula:
x = [22 +- sqrt(22^2 - 4*117)]/2
x = [22 +- sqrt(16)]/2
Positive solution:
x = [11 + 2] = 13 (width)
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Since x+y = 22, y = 22-13 = 9 (length)
============================================
Cheers,
Stan H.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
LW=117
L=117/W
2L+2W=44
2(117/W)+2W=44
234/W+2W=44
(234+2W^2/W=44
(234+2W^2)/W=44
2W^2+234=44W
2W^2-44W+234=0
2(W^2-22W+117)=0
2(W-13)(W-9)=0
W-13=0
W=13 ANS.
L*13=117
L=117/13
L=9 ANS
2*9+2*13=44
18+26=44
44=44
PROOF:

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