document.write( "Question 722822: An architect is designung a building with a right triangle footprint. The hypotenuse of the triangle is 80 feet longer than one leg of the triangle and 40 feet longer than the other leg. Use Pythagorean Theorem to find the dimensions of the footprint of the building. \n" ); document.write( "

Algebra.Com's Answer #442927 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x\"$ = length of the hypotenuse (in feet)
\n" ); document.write( " $\"x-80\"$ = length (in feet) of one leg of the triangle, and
\n" ); document.write( " $\"x-40\"$ = length (in feet) of one leg of the triangle
\n" ); document.write( "must be positive numbers.
\n" ); document.write( "
\n" ); document.write( "The Pythagorean Theorem says that
\n" ); document.write( " $\"%28x-80%29%5E2%2B%28x-40%29%5E2=x%5E2\"$ --> $\"x%5E2-160x%2B6400%2Bx%5E2-80x%2B1600=x%5E2\"$ --> $\"2x%5E2-240x%2B8000=x%5E2\"$ --> $\"x%5E2-240x%2B8000=0\"$
\n" ); document.write( "
\n" ); document.write( "We can solve that quadratic equation by factoring, or by \"completing the square\", or by using the quadratic formula.
\n" ); document.write( "
\n" ); document.write( "By factoring:
\n" ); document.write( " $\"x%5E2-240x%2B8000=0\"$ --> $\"%28x-200%29%28x-40%29=0\"$ --> $\"x=200\"$ or $\"x=40\"$
\n" ); document.write( "
\n" ); document.write( "Completing the square:
\n" ); document.write( " $\"x%5E2-240x%2B8000=0\"$ --> $\"x%5E2-240x=-8000\"$ --> $\"x%5E2-240x%2B120%5E2=120%5E2-8000\"$ --> $\"%28x-120%29%5E2=14400-8000\"$ --> $\"%28x-120%29%5E2=6400\"$ --> $\"%28x-120%29%5E2=80%5E2\"$ --> $\"x=120+%2B-+80\"$ --> $\"x=200\"$ or $\"x=40\"$
\n" ); document.write( "
\n" ); document.write( "Using the quadratic formula:
\n" ); document.write( " $\"x%5E2-240x%2B8000=0\"$ --> $\"x+=+%28-%28-240%29+%2B-+sqrt%28%28-240%29%5E2-4%2A1%2A8000%29%29%2F%282%2A1%29+\"$ --> $\"x+=+%28240+%2B-+sqrt%2857600-32000%29%29%2F2\"$ --> $\"x+=+%28240+%2B-+sqrt%2825600%29%29%2F2\"$ --> $\"x+=+%28240+%2B-+160%29%2F2\"$ --> $\"x=120+%2B-+80\"$ --> $\"x=200\"$ or $\"x=40\"$
\n" ); document.write( "
\n" ); document.write( " $\"x=200\"$ yields $\"x-80=120\"$ and $\"x-40=160\"$ for a building with sides measuring $\"highlight%28120%29\"$ , $\"highlight%28160%29\"$ , and $\"highlight%28200%29\"$ feet.
\n" ); document.write( " $\"x=40\"$ is a solution to the quadratic equation, but it is not a solution to the problem, because it yields negative numbers for $\"x-80\"$ and $\"x-40\"$ and those negative numbers cannot be the lengths of the sides of a building. \n" ); document.write( "

\n" );