1. ## help with question

1.A right triangle has an area of 25 cm^2. express the hypotenuse, h, of this triangle as a function of its perimeter, p

2.Find |m|
Root3(m+9)=3 + Root3(m-9)

thanks for the help

2. Hello, monkius!

1.A right triangle has an area of 25 cm².
Express the hypotenuse, $\displaystyle h$, of this triangle as a function of its perimeter, $\displaystyle p.$
Code:
      *
|  *    h
b |     *
|        *
* - - - - - *
a

The area is 25 cm²: .$\displaystyle \frac{1}{2}ab = 25 \quad\Rightarrow\quad ab = 50$

The perimeter is: .$\displaystyle p \:=\:a+b+h \quad\Rightarrow\quad a + b \:=\:p -h$ .[1]

Square both sides of equation [1]: .$\displaystyle (a+b)^2 \:=\:(p-h)^2$

And we have: .$\displaystyle a^2 + 2ab + b^2 \:=\:p^2 - 2 ph + h^2$

. . or: .$\displaystyle \underbrace{(a^2+b^2)}_{\text{This is }h^2} \;+ \;2\underbrace{(ab)}_{\text{This is 50}} \:=\:p^2 - 2ph + h^2$

So we have: .$\displaystyle h^2 + 100 \;=\;p^2 - 2ph + h^2 \quad\Rightarrow\quad 2ph \:=\:p^2-100$

Therefore: .$\displaystyle \boxed{h \;=\;\frac{p^2-100}{2p} }$