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Question 71427: the length of a rectangle is 3 times the width. If the width were increased by 4 and the length remains the same the resulting rectangle would have an area of 231 sq.inches. find the dimension of the original.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The length of a rectangle is 3 times the width. If the width were increased by 4 and the length remains the same the resulting rectangle would have an area of 231 sq.inches. find the dimension of the original.
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The dimensions of the original:
Let x = width
Then 3x = length
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Dimensions of the larger rectangle:
(x+4) = width, (original width increased by 4)
3x = length, (remains the same)
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Area of larger:
3x(x+4) = 3x^2 + 12x
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"resulting rectangle would have an area of 231"
3x^2 + 12x = 231
3x^2 + 12x - 231 = 0; our old friend, the quadratic equation
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Simplify, divide equation by 3:
x^2 + 4x - 77 = 0
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Easily factors to:
(x+11)(x-7) = 0
x = +7, the solution we want here
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Original rectangle: 7 by 3(7);
21 by 7 ft
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Check: using the area of 231:
21 * (7+4) = 231
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