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

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- Aug 31st 2012, 12:51 PMmido22problem 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

Attachment 24659 - Aug 31st 2012, 02:15 PMMaxJasperRe: 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!!!!!!?!??!

- Aug 31st 2012, 07:39 PMSorobanRe: problem in solid geometry
Hello, mido22!

Quote:

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

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

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

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

- Sep 1st 2012, 02:51 PMmido22Re: 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 - Sep 1st 2012, 02:53 PMmido22Re: 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 >>:(