+0

0
357
6
+238

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

#4
+85644
+10

matsunnymat

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
Sort:

#1
+1311
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
+85644
+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
#3
+238
0

matsunnymat  Aug 25, 2015
#4
+85644
+10

matsunnymat

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
+1311
+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
#6
+85644
0

Dragonlance, you usually give good answers.......we mods aren't always correct, either....I seem to remember a few days ago that you spotted one of my errors on a Physics question....!!!!

CPhill  Aug 25, 2015

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