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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Triangle ABC has a right angle at B. Point D is the foot of the altitu

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Math Expert V
Joined: 02 Sep 2009
Posts: 59236
Triangle ABC has a right angle at B. Point D is the foot of the altitu  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 43% (03:12) correct 57% (03:10) wrong based on 37 sessions

### HideShow timer Statistics Triangle ABC has a right angle at B. Point D is the foot of the altitude from B, AD = 3, and DC = 4. What is the area of triangle ABC ?

(A) $$4\sqrt{3}$$

(B) $$7\sqrt{3}$$

(C) 21

(D) $$14\sqrt{3}$$

(E) 42

Attachment: 4bea2faf81f4ba6dca40fdb9ce720c9ed82b168c.png [ 5.59 KiB | Viewed 619 times ]

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Math Expert V
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Re: Triangle ABC has a right angle at B. Point D is the foot of the altitu  [#permalink]

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TheNightKing wrote:
chetan2u Can you help with this one?

I believe Ypsychotic is saying CD/BD=BD/AD. From this we can find BD and with that we can find area.

Hi,

Yes similar triangle property can be used to find BF and as you too have mentioned that BD =$$\sqrt{AD*CD}=\sqrt{12}$$ and I too will do it same way.

But even the choices give away the answer and we should be able to exploit this too.
The area is $$\frac{1}{2}*7*BD$$.
So our answer should normally be multiple of 7.
A is out.
Now take C. If (1/2)*7*BD=21...BD=6
But is it possible .. NO as in triangle aBDC, BC will become >7, that is a side of a right angled triangle will become bigger than the hypotenuse AC or 3+4.
So answer is less than 21 for sure. Only B left.
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Re: Triangle ABC has a right angle at B. Point D is the foot of the altitu  [#permalink]

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Bunuel wrote: Triangle ABC has a right angle at B. Point D is the foot of the altitude from B, AD = 3, and DC = 4. What is the area of triangle ABC ?

(A) $$4\sqrt{3}$$

(B) $$7\sqrt{3}$$

(C) 21

(D) $$14\sqrt{3}$$

(E) 42

Attachment:
4bea2faf81f4ba6dca40fdb9ce720c9ed82b168c.png

Angle ACD=Angle BAD, Because if Angle c=x, angle a= 90.-x, in Triangle ABD, Angle ABD=180-(90+90-x)
=x, Similarly, Angle BCD= Angle ABD,

Using Similarlity,

$$\frac{4}{x}=\frac{x}{3}$$

$$x=2\sqrt{3}$$

$$Area=1/2*2\sqrt{3}*(4+3)=7\sqrt{3}$$

IMO, Option B
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Re: Triangle ABC has a right angle at B. Point D is the foot of the altitu  [#permalink]

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chetan2u Can you help with this one?

I believe Ypsychotic is saying CD/BD=BD/AD. From this we can find BD and with that we can find area.

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You are missing on great learning if you don't know what this is: Project SC Butler Re: Triangle ABC has a right angle at B. Point D is the foot of the altitu   [#permalink] 16 Oct 2019, 09:45
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