document.write( "Question 232478: howto find the area of the 45-45-90 triangle with a hypotenuse of 24? \n" ); document.write( "

Algebra.Com's Answer #171792 by Earlsdon(6294) $\"\"$ $\"About$

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First, this right triangle is an isosceles triangle.
\n" ); document.write( "How do we know this? The triangle has two of its angles equal while the third angle is a right angle so it must be an isosceles triangle thus the two legs are equal.
\n" ); document.write( "Let's call the length of one leg = x.
\n" ); document.write( "By the Pythagorean theorem, we can say:
\n" ); document.write( " $\"24%5E2+=+x%5E2%2Bx%5E2\"$ Simplifying this we get:
\n" ); document.write( " $\"576+=+2%2Ax%5E2\"$ Dividing both sides by 2, we have:
\n" ); document.write( " $\"288+=+x%5E2\"$ Rewrite the left side then take the square root of both sides.
\n" ); document.write( " $\"sqrt%282%2A144%29+=+sqrt%28x%5E2%29\"$
\n" ); document.write( " $\"12%2Asqrt%282%29+=+x\"$ or $\"highlight_green%28x+=+12%2Asqrt%282%29%29\"$
\n" ); document.write( "For this triangle, the area is given by:
\n" ); document.write( " $\"A+=+%281%2F2%29%28b%2Ah%29\"$ where b = x and h = x.
\n" ); document.write( " $\"A+=+%281%2F2%29%28x%5E2%29\"$ Substitute $\"x%5E2+=+288\"$ from above.
\n" ); document.write( " $\"A+=+%281%2F2%29%28288%29\"$
\n" ); document.write( " $\"highlight%28A+=+144%29\"$ sq. units.
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