document.write( "Question 1002047: The sum of the lengths of the two perpendicular sides of a right triangle is 30 centimeters. What are their lengths if the square of the hypotenuse is a minimum? \n" ); document.write( "

Algebra.Com's Answer #619078 by MathTherapy(10552) $\"\"$ $\"About$

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The sum of the lengths of the two perpendicular sides of a right triangle is 30 centimeters. What are their lengths if the square of the hypotenuse is a minimum?
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The square of the hypotenuse is the sum of the squares of the legs
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document.write( "Therefore, their sum is 30, and the hypotenuse (SUM OF THEIR SQUARES) is a minimum (you may recall that: )\r
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document.write( "Let longer leg be x, and shorter, y
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document.write( "Then we have: x + y = 30______y = - x + 30 ------- eq (i)
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document.write( "Also,  -------- eq (ii)
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document.write( " ------- Substituting - x + 30 for y in eq (ii)
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document.write( "MINIMUM occurs at: x = , or at: , or at , or at: x = 15
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document.write( "With MINIMUM occurring at x = 15, we get: 
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document.write( "y = - 15 + 30 ----------- Substituting 15 for x in eq (i)
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document.write( "y = 15
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document.write( "Thus, length of each leg is:  cm  \n" );
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