help about right triangles!

hello!

i have question about right triangles and perimeter:

"If the perimeter of a right triangle is 12 and it's hypotenuse is 5, what is the area of the triangle?"

formula for area: a=bh/2

perimeter = b+h+hypotenuse = 12

this is solved by substitution?

b+h+5=12

b+h=7

b=7/h

a=bh/2

a=[(7/h)h]/2

a=7/2

a=3.5

Re: help about right triangles!

Let $\displaystyle a$ and $\displaystyle b$ be the two legs of the right triangle. Since the perimeter is 12 and the hypotenuse is 5, we know:

$\displaystyle a+b=7$

By the Pythagorean theorem, we also know:

$\displaystyle a^2+b^2=5^2$

I recommend squaring the first equation to find $\displaystyle ab$, since the second equation gives you the value of the sum of the squares of the legs.