document.write( "Question 198854: Triangle RAT is an isoceles right triangle with right angle T and area 50 cm. squared. find the lengths of the legs and hypotenuse. \n" ); document.write( "

Algebra.Com's Answer #149371 by Earlsdon(6294) $\"\"$ $\"About$

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Start with the formula for the area of a triangle:
\n" ); document.write( " $\"A+=+%281%2F2%29b%2Ah\"$ In an isosceles triangle, as in this problem, the b and h are equal, let's call them x, and the area is given as 50sq.cm., so...
\n" ); document.write( " $\"50+=+%281%2F2%29%28x%2Ax%29\"$ Multiply both sides by 2.
\n" ); document.write( " $\"100+=+x%5E2\"$ Take the square root of both sides.
\n" ); document.write( " $\"x+=+10\"$
\n" ); document.write( "Each of the legs is 10 cm.
\n" ); document.write( "The hypotenuse (c) can be found by the Pythagorean theorem: $\"c%5E2+=+a%5E2%2Bb%5E2\"$ , where a = 10cm. and b = 10cm.
\n" ); document.write( " $\"c%5E2+=+10%5E2%2B10%5E2\"$
\n" ); document.write( " $\"c%5E2+=+100%2B100\"$
\n" ); document.write( " $\"c%5E2+=+200\"$ Take the square root of both sides.
\n" ); document.write( " $\"c+=+sqrt%28200%29\"$
\n" ); document.write( " $\"c+=+14.14\"$ cm. Approx. \n" ); document.write( "

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