SOLUTION: A rectangle is 10 cm longer than it is wide. A line segment cuts the area enclosed into two pieces, one of which is a square. The area of the rectangle is 118cm squared more than t

Algebra ->  Parallelograms -> SOLUTION: A rectangle is 10 cm longer than it is wide. A line segment cuts the area enclosed into two pieces, one of which is a square. The area of the rectangle is 118cm squared more than t      Log On


   

Question 66513: A rectangle is 10 cm longer than it is wide. A line segment cuts the area enclosed into two pieces, one of which is a square. The area of the rectangle is 118cm squared more than the area of the square. What is the width of the rectangle?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangle is 10 cm longer than it is wide. A line segment cuts the area enclosed into two pieces, one of which is a square. The area of the rectangle is 118cm squared more than the area of the square. What is the width of the rectangle?
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Let x = the width of the rectangle; (x+10) = the length
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The square sides would = x, it's area would be x^2
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"The area of the rectangle is 118 cm squared more than the area of the square."
Means the Area of the rectangle = (x^2 + 118)
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We also know that the Area of the rectangle = x(x+10)= (x^2 + 10x)
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Therefore:
x^2 + 10x = x^2 + 118
x^2 - x^2 + 10x = 118
10x = 118
x = 11.8 cm is the width
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Check:
11.8^2 + 118 = 257.24
11.8 * 21.8 = 257.24 sq cm