SOLUTION: A rectangle is 15 cm wide and 18 cm long. If both dimensions are decreased by the same amount, the area of the new rectangle formed is 116 cm^2 less than the area of the original.
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-> SOLUTION: A rectangle is 15 cm wide and 18 cm long. If both dimensions are decreased by the same amount, the area of the new rectangle formed is 116 cm^2 less than the area of the original.
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Question 163541This question is from textbook
: A rectangle is 15 cm wide and 18 cm long. If both dimensions are decreased by the same amount, the area of the new rectangle formed is 116 cm^2 less than the area of the original. Find the dimensions of the new rectangle. This question is from textbook
You can put this solution on YOUR website! A rectangle is 15 cm wide and 18 cm long. If both dimensions are decreased by the same amount, the area of the new rectangle formed is 116 cm^2 less than the area of the original. Find the dimensions of the new rectangle.
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Original rectangle area: 15 * 18 = 270 sq/cm
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Let x = amt each dimension is decreased:
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Area of new rectangle
(15-x)(18-x) = 270 - 33x + x^2
:
Original rectangle - new rectangle = 116 sq/cm
270 - (270 - 33x + x^2) 116
270 - 270 + 33x - x^2 = 116
Arrange as a quadratic on the right
0 = x^2 - 33x + 116
Factor this to:
(x - 4)(x - 29) = 0
x = 4 cm; is the only solution that makes sense.
:
:
New rectangle 11 * 14 = 154
270 - 154 = 116; confirms our solution
