(p^2 - (2)(17)(p) + (2)17^2)/((2)(p - 17))

any justifications? or should i just blame the online hw system for screwin me up haha

thx a lot by the way everyone . you guys are awesome

]]>MathsIsFun wrote:

p-a-h

It's right, as far as I can tell, but it just annoys me when things can't be simplified and you have to leave them in a mess like that. The best alternative I could come up with is:

h = (p-a)/2 - a²/2(p-a)

But that's not really any simpler. Maybe a little bit.

]]>We know one of them is 17 cm, let's call that side "a"

Another side can be called "b"

And the hypotenuse is already called "h"

The perimeter is a+b+h

And we also know that a²+b²=h² (Pythagoras Theorem)

So, we have two formulas:

p=a+b+h

a²+b²=h²

Lets start with Pythagoras:

h²=a²+b²

And the perimeter formula can be used to find b

p=a+b+h ==> b = p-a-h

So:

h² = a²+b² = a²+(p-a-h)² = a²+(p-a-h)²

It is looking like it is going to very complicated!

Expanding: (p-a-h)² = p² - 2ap - 2hp + 2ha +a² + h²

So: h² = a² + p² - 2ap - 2hp + 2ha +a² + h²

Simplifying: 0 = a² + p² - 2ap - 2hp + 2ha +a²

Put "h" terms on left: 2hp - 2ha = a² + p² - 2ap +a²

Simplify: 2h(p-a) = 2a² + p² - 2ap

And last: h = (2a² + p² - 2ap) / 2(p-a)

(I hope!)

(You can put in a value of 17 for a if you want)

]]>"The altitude of a right triangle is 17 cm. Let h be the length of the hypotenuse and let p be the perimeter of the triangle. Express h as a function of p ."

h(p):_________________

]]>