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Math Expert V
Joined: 02 Sep 2009
Posts: 59095
What is the area of the triangle ABC?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 66% (02:00) correct 34% (01:56) wrong based on 35 sessions

### HideShow timer Statistics What is the area of the triangle ABC?

(A) 15

(B) $$15\sqrt{3}$$

(C) $$\frac{5\sqrt{119}}{2}$$

(D) 32.5

(E) 36

Attachment: Capture1 (1).JPG [ 7.33 KiB | Viewed 518 times ]

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Director  G
Joined: 22 Nov 2018
Posts: 562
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Re: What is the area of the triangle ABC?  [#permalink]

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Bunuel wrote: What is the area of the triangle ABC?

(A) 15

(B) $$15\sqrt{3}$$

(C) $$\frac{5\sqrt{119}}{2}$$

(D) 32.5

(E) 36

Attachment:
Capture1 (1).JPG

The altitude to the base from A will form a 30-60-90 triangle with Hypo as 12. So Other altitude using 1-root3-2 will be 6root3 (as opposite 60degrees) so area is 15root3 IMO B
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VP  D
Joined: 20 Jul 2017
Posts: 1076
Location: India
Concentration: Entrepreneurship, Marketing
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Re: What is the area of the triangle ABC?  [#permalink]

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1
Bunuel wrote: What is the area of the triangle ABC?

(A) 15

(B) $$15\sqrt{3}$$

(C) $$\frac{5\sqrt{119}}{2}$$

(D) 32.5

(E) 36

Attachment:
The attachment Capture1 (1).JPG is no longer available Draw a perpendicular from point C to meet side AB at point D

CDB is a 30-60-90 triangle with
∠C = 30 deg, ∠D = 90 deg & ∠B = 60 deg

--> BD: CD: BC = 1: $$\sqrt{3}$$: 2
--> BD = k, CD = $$\sqrt{3}$$k, BC = 2k
Given BC = 2k = 5
--> k = 5/2

Altitude = $$\sqrt{3}$$k = 5/2*$$\sqrt{3}$$

Area of triangle ABC = 1/2*base*height = 1/2*AB*CD
= 1/2*12*5/2*$$\sqrt{3}$$
= 15$$\sqrt{3}$$

IMO Option B

Pls Hit Kudos if you like the solution
Attachments 33.png [ 35.79 KiB | Viewed 532 times ]

ISB School Moderator G
Joined: 08 Dec 2013
Posts: 606
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Re: What is the area of the triangle ABC?  [#permalink]

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1
Bunuel wrote: What is the area of the triangle ABC?

(A) 15

(B) $$15\sqrt{3}$$

(C) $$\frac{5\sqrt{119}}{2}$$

(D) 32.5

(E) 36

Attachment:
The attachment Capture1 (1).JPG is no longer available

AD= 6 Root(3) by 60-90-30 Triangle Properties

Now, Area= (1/2) * 5 * 6(Root 3)
Attachment: Capture.PNG [ 44.3 KiB | Viewed 368 times ]

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I never gave up what I wanted- Re: What is the area of the triangle ABC?   [#permalink] 21 Jun 2019, 02:44
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# What is the area of the triangle ABC?  