SOLUTION: howto find the area of the 45-45-90 triangle with a hypotenuse of 24?

Question 232478: howto find the area of the 45-45-90 triangle with a hypotenuse of 24?
Found 2 solutions by rfer, Earlsdon:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
A=.5Lh
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a^2+b^2=c^2
a^2+b^2=24^2
a^2+b^2=576
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legs are equal so divide 576 by 2 then take the sq rt
576/2=288
sq rt of 288=16.97
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A=.5Lh
A=.5*16.97*16.97
A=144 sq units

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
First, this right triangle is an isosceles triangle.
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.
Let's call the length of one leg = x.
By the Pythagorean theorem, we can say:
Simplifying this we get:
Dividing both sides by 2, we have:
Rewrite the left side then take the square root of both sides.

or
For this triangle, the area is given by:
where b = x and h = x.
Substitute from above.

sq. units.

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