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# Triangle ABC has a right angle at B. Point D is the foot of the altitu

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Math Expert
Joined: 02 Sep 2009
Posts: 54375
Triangle ABC has a right angle at B. Point D is the foot of the altitu  [#permalink]

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28 Mar 2019, 05:55
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Difficulty:

95% (hard)

Question Stats:

29% (03:40) correct 71% (02:57) wrong based on 14 sessions

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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 228 times ]

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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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28 Mar 2019, 19:48
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] 28 Mar 2019, 19:48
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