SOLUTION: One of my Homework Questions is Find the area of a isosceles right triangle with a hypotnuse of 10 cm. I know to get from hyp to short leg you divide by 2 ( 5) and since it is isos

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Question 253030: One of my Homework Questions is Find the area of a isosceles right triangle with a hypotnuse of 10 cm. I know to get from hyp to short leg you divide by 2 ( 5) and since it is isosceles I'm assuming that the other leg is 5 then you would just do 1/2 ( 5 * 5 ) but don't the long and short leg together have to be greater than the hyp? I'm so confused. Please help.
Found 2 solutions by richwmiller, JimboP1977:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
The usual Pythagorean theorem formula for a right triangle is a^2+b^2=c^2
where the hypotenuse is c and here it is c=10
but since a =b we can make it
2a^2=c^2
so
2a^2=10^2
2a^2-=100
divide by 2
a^2=50
It just so happens we can stop here since the area of a triangle is 1/2 bh
and in our isosceles triangle the base and height are the same.
So, 1/2 bh becomes 1/2 a^2
1/2 a^2=50/2=25
area =25cm^2

Answer by JimboP1977(311) (Show Source):
You can put this solution on YOUR website!
Reading this may help you: http://mathworld.wolfram.com/IsoscelesTriangle.html
In an isosceles right angled triangle the adjacent and opposite sides (the sides that are not the hypotenuse) are the same length.
Using Pythagoras we have hypotenuse^2 = adajacent^2+opposite^2
Since the two sides are the same we can say that h^2=2*a^2
100 = 2*a^2
50=a^2
a=sqrt50
The area of a triangle is equal to half times base times height. So the area is 1/2*sqrt50*sqrt50 = 1/2*50 = 25