document.write( "Question 355099: One of the legs of a right triangle has length √19 cm The sum of the lengths of the hypotenuse and the other leg is 19 cm. What is the area of this triangle in square centimeters? \n" ); document.write( "

Algebra.Com's Answer #253619 by robertb(5830) $\"\"$ $\"About$

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The legs have measure $\"sqrt%2819%29\"$ and b, the hypotenuse, c. We have to find the area $\"A+=+b%2Asqrt%2819%29%2F2\"$ . It is given that $\"b%2Bc+=+19\"$ , and so $\"c+=+19-b\"$ . From the Pythagorean theorem, $\"%28sqrt%2819%29%29%5E2%2Bb%5E2+=+c%5E2\"$ , or
\n" ); document.write( " $\"19%2Bb%5E2+=+c%5E2\"$ .\r
\n" ); document.write( "\n" ); document.write( "By direct substitution,
\n" ); document.write( " $\"19+%2B+b%5E2+=+%2819-b%29%5E2\"$ ,
\n" ); document.write( " $\"19+%2B+b%5E2+=+19%5E2+-+38b%2Bb%5E2\"$ ,
\n" ); document.write( " $\"19+=+19%5E2+-+38b\"$ ,
\n" ); document.write( " $\"38b+=+19%5E2+-+19\"$ ,
\n" ); document.write( " $\"2b+=+19+-+1\"$ , after dividing both sides by 19.
\n" ); document.write( " $\"b+=+9\"$ . This area is then $\"A+=9%2Asqrt%2819%29%2F2\"$ sq. cm. \n" ); document.write( "

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