document.write( "Question 1040514: The hypotenuse of a right triangle is 12 inches and the area is 24 square inches. Find the dimension of the triangle, correct to one decimal place. \n" ); document.write( "

Algebra.Com's Answer #655336 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+A+\"$ = the area of the right triangle in square inches
\n" ); document.write( "Let $\"+b+\"$ = the base of the right triangle in inches
\n" ); document.write( "Let $\"+c+\"$ = the height of the right triangle in inches
\n" ); document.write( "----------------------------------------------
\n" ); document.write( " $\"+A+=+%281%2F2%29%2Ab%2Ac+\"$
\n" ); document.write( " $\"+24+=+%281%2F2%29%2Ab%2Ac+\"$
\n" ); document.write( " $\"+b%2Ac+=+48+\"$
\n" ); document.write( " $\"+c+=+48%2Fb+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "Use pythagorean theorem
\n" ); document.write( "

\n" ); document.write( " $\"+b%5E4+%2B+2304+=+144b%5E2+\"$
\n" ); document.write( " $\"+144b%5E2+-+b%5E4+=+2304+\"$
\n" ); document.write( "Let $\"+z+=+b%5E2+\"$
\n" ); document.write( " $\"+-z%5E2+%2B+144z+-+2304+=+0+\"$
\n" ); document.write( "Use quadratic formula
\n" ); document.write( " $\"+z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+-1+\"$
\n" ); document.write( " $\"+b+=+144+\"$
\n" ); document.write( " $\"+c+=+-2304+\"$
\n" ); document.write( " $\"+z+=+%28+-144+%2B-+sqrt%28+144%5E2-4%2A%28-1%29%2A%28-2304%29+%29%29%2F%282%2A%28-1%29%29+\"$
\n" ); document.write( " $\"+z+=+%28+-144+%2B-+sqrt%28+20736+-+9216+%29%29%2F%28%28-2%29+%29+\"$
\n" ); document.write( " $\"+z+=+%28+-144+%2B-+sqrt%28+11520+%29+%2F+%28-2%29+%29+\"$
\n" ); document.write( " $\"+z+=+%28+-144+%2B+107.3313+%29+%2F+%28-2%29+\"$
\n" ); document.write( " $\"+z+=+36.6687%2F2+\"$
\n" ); document.write( " $\"+z+=+18.3344+\"$
\n" ); document.write( "and, also:
\n" ); document.write( " $\"+z+=+%28+-144+-+107.3313+%29+%2F+%28-2%29+\"$
\n" ); document.write( " $\"+z+=+251.3313%2F2+\"$
\n" ); document.write( " $\"+z+=+125.6657+\"$
\n" ); document.write( "Since $\"+z+=+b%5E2+\"$
\n" ); document.write( " $\"+b+=+sqrt%28z%29+\"$
\n" ); document.write( " $\"+b+=+sqrt%28+18.3344+%29+\"$
\n" ); document.write( " $\"+b+=+4.2819%0D%0Aand%0D%0A%7B%7B%7B+c+=+48%2Fb+\"$
\n" ); document.write( " $\"+c+=+48%2F4.2819+\"$
\n" ); document.write( " $\"+c+=+11.21+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+24+=+%281%2F2%29%2Ab%2Ac+\"$
\n" ); document.write( " $\"+48+=+b%2Ac+\"$
\n" ); document.write( " $\"+48+=+4.2819%2A11.21+\"$
\n" ); document.write( " $\"+48+=+48.0001+\"$
\n" ); document.write( "close enough
\n" ); document.write( "----------------------
\n" ); document.write( "

\n" ); document.write( " $\"+144+=+143.9988+\"$
\n" ); document.write( "close enough
\n" ); document.write( "-----------------------
\n" ); document.write( "The triangle is:
\n" ); document.write( "12 x 4.3 x 11.2
\n" ); document.write( "Hope I got it! \n" ); document.write( "

\n" );