# Thread: problem in solid geometry

1. ## problem in solid geometry

if ABC is a triangle where AB = 5cm , AC = 3cm , D is the midpoint of BC and draw AH = (6 *root 2)cm perpendicular to both AC and AB . find the length of DH

2. ## Re: problem in solid geometry

Image is wrong if AH=6*squrt(2)=8.485 cm. Is AH perpendicular to BC? You say it is prep to both AC & AB!!!!!!?!??!

3. ## Re: problem in solid geometry

Hello, mido22!

ABC is a triangle where AB = 5cm, AC = 3cm, D is the midpoint of BC.
Draw AH = 6√2 cm, perpendicular to both AC and AB.
Find the length of DH.

The diagram looks like this.
Code:
            H
o
| *
*|  _*
|6√2 *
* |       *
|         *
*  o - - - - - o B
*A    5   *
* *       *
*3    o
**   *   D
* *
o
C
I don't see a unique length for $\displaystyle D\!H.$

It depends on $\displaystyle \theta = \angle B\!AC.$

If $\displaystyle \theta = 0^o,\:D\!H = 7\sqrt{2}$

If $\displaystyle \theta = 180^o,\:D\!H = 6\sqrt{2}$

4. ## Re: problem in solid geometry

sorry i forgot to write that BC = 7 cm

<BAC not zero and not 180

i have a final answer that HD = 2.5 but i can't find a proof

5. ## Re: problem in solid geometry

i can prove that AH is perpendicular to BC since it is perpendicular to both AB , AC but then i don't know >>