Question 142751: The area of a room is 20 square metre. If the length is increased by 3 metre and the width is increased by 1 metre, the room will double in area. Determine the original dimensions of the room.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The area of a room is 20 square metre. If the length is increased by 3 metre and the width is increased by 1 metre, the room will double in area. Determine the original dimensions of the room.
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lw = 20
(l+3)(w+1) = 40
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lw + l + 3w + 3 = 40
20 + l + 3w + 3 = 40
l + 3w = 17
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But l = 20/w
(20/w) + 3w = 17
20 + 3w^2 = 17w
3w^2 - 17w + 20 = 0
w = [17 +- sqrt(17^2 - 4*3*20)]/6
w = [17 +- sqrt(49)]/6
w = [17+-7]/6
w = 4 or w = 5/3
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If width = 4, then length = 5
This answer checks out.
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If width = 5/3,
lw = 20
l(5/3) = 20
l = 12
This is wrong.
Therefore w = 5/3 is an extraneous answer.
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Cheers,
Stan H
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