SOLUTION: the perimeter of a rectangle is 24 cm. the area of the same rectangle is 20 sq. cm. find the sides of the rectangle without using calculus.
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Question 313679: the perimeter of a rectangle is 24 cm. the area of the same rectangle is 20 sq. cm. find the sides of the rectangle without using calculus. Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website! 24=2L+2W
20=LW OR L=20/W
REPLACING L IN THE FIRST EQUATION BY (20/W) & SOLVE FOR W.
24=2(20/W)+2W
24=40/W+2W
24=(40+2W*W)/W
24=(40+2W^2)/W CROSS MULTIPLY.
24*W=40+2W^2
24W=40+2W^2
2W^2-24W+40=0
2(W^2-12W+20)=0
2(W-10)(W-2)=0
W-10=0
W=10 ANS.
L=20/10=2 ANS.
W-2=0
W=2 ANS.
L=20/2=10 ANS.
PROOF:
20=2*10
20=20
24=2*10+2*2
24=20+4
24=24
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