document.write( "Question 821306: The diagonal of a rectangle is 15 feet and the width is 9 feet. Find the area of the rectangle \n" ); document.write( "

Algebra.Com's Answer #494062 by KMST(5328) $\"\"$ $\"About$

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The diagonal splits the rectangle into two congruent right triangles.
\n" ); document.write( "In each of those triangles, the hypotenuse is the diagonal of the rectangle,
\n" ); document.write( "one leg is the width of the rectangle,
\n" ); document.write( "and the other leg in the length of the rectangle.
\n" ); document.write( "If the length is $\"x\"$ $\"feet\"$ , according to the Pythagorean theorem,
\n" ); document.write( " $\"x%5E2%2B9%5E2=15%5E2\"$
\n" ); document.write( " $\"x%5E2%2B81=225\"$
\n" ); document.write( " $\"x%5E2=225-81\"$
\n" ); document.write( " $\"x%5E2=144\"$
\n" ); document.write( " $\"x%5E2=12%5E2\"$
\n" ); document.write( "So the length of the rectangle is $\"12+feet\"$ .
\n" ); document.write( " $\"x=-12\"$ is another solution of $\"x%5E2=12%5E2\"$ , but lengths are never negative numbers.
\n" ); document.write( "
\n" ); document.write( "The area of a rectangle with a length of $\"12+feet\"$ and a width of $\"9+feet\"$ is
\n" ); document.write( " $\"%289feet%29%2812+feet%29=highlight%28108%29\"$ $\"square\"$ $\"feet\"$ . \n" ); document.write( "

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