abd is an isosceles triangle of base 30 cm .the altitude to the base is 20cm.the length of the other altitude (in cm)is???

matsunnymat
Aug 24, 2015

#1**0 **

I think triangles only have 1 altitude so I guess you mean what is the length of one of the sides.

a and c is the sides and c is the base and h is height.

then

$${\mathtt{a}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\sqrt{{{\mathtt{b}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{h}}}^{{\mathtt{2}}}\right)}}$$

$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\sqrt{{{\mathtt{30}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{20}}}^{{\mathtt{2}}}\right)}} = {\mathtt{25}}$$

Dragonlance
Aug 24, 2015

#2**+10 **

Dragonlance .....we actually have two more congruent altitudes.......

See the following picture.......

Draw altitude AE to side BD......

Note that ΔCBD ≈ ΔEBA so

BD/DC = BA/AE

25/20 = 30/AE → AE = 30*20/25 = 24

And we would have another congruent altitude to this one drawn from B to side AD

CPhill
Aug 24, 2015

#4**+10 **

Best Answer

I believe that my answer is correct....there are 2 different altitudes.....the given one of 20 and the other that I found of 24 [ The other altitude, as I pointed out, is also 24]

P.S. .... Dragonlance gave the correct side length, but this isn't an altitude

CPhill
Aug 25, 2015

#5**+5 **

Sorry. I thought maybe it do have three because there are three angles in a triangle. But I look at about 20 questions on maths sites that have altitude or height as part of the problem and it only ever have one altitude part, so I didn’t know. But I do now. :)

A good thing to know is if a mod have a answer different from someone else then the mod is usually right. They always say so if they make a mistake and they not make very many anyway.

Dragonlance
Aug 25, 2015