I've been trying to work this problem. i just can't figure it out. "the base of an isosceles triangle is half as long as the two equal sides. write the area of the triangle as a function of the length of the base"

Question

danjs · Answer

|dw:1454966740603:dw|

danjs · Answer

You recall the area is 

A = 1/2 * base * height


draw this line angle bisector ant a right angle forms with the base

danjs · Answer

|dw:1454966909326:dw|

danjs · Answer

that all appear straight forward so far

anonymous · Answer

ah, now i understand.

anonymous · Answer

mann, that was easier than i thought. thanks so much.

phi · Answer

although because they want the area in terms of the base, I would label the base x and a the two equal sides 2x.

danjs · Answer

yeah i was gonna say that, but figured wait till the end.. . seems like you got it though

phi · Answer

using ½ * base * height  you get x/2 * h
you need to find h "in terms of " x

danjs · Answer

as is , the function will have (x/2) terms,if you change the original base to x and the sides 2x,  

the area function will have x terms,   the overall value is still the same, h will be a bit diff from the pythagoraen calculation

phi · Answer

yes, but if you label the base x/2  the answer will be in terms of the other side
i.e. the expression won't be the one they want.

danjs · Answer

less you write the final function as

$$\sqrt{15}\frac{ x^2 }{ 4 }  ---> \sqrt{15}*(\frac{ x }{ 2 })^2$$

right


A(x/2),   i know it is not as nice

danjs · Answer

maybe not, i see, still defined as half the side, 

side in terms of the base x is better