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# What is the area of the triangle ABC?

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Manager
Joined: 03 Mar 2018
Posts: 182
What is the area of the triangle ABC?  [#permalink]

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15 Mar 2018, 08:56
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:44) correct 30% (01:30) wrong based on 34 sessions

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What is the area of the triangle ABC?

(A) 15
(B) $$15\sqrt{3}$$
(C) $$5\sqrt{119}/2$$
(D) 32.5
(E) 36

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Intern
Joined: 06 Oct 2017
Posts: 9
What is the area of the triangle ABC?  [#permalink]

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15 Mar 2018, 15:05
Let AH be the height of the triangle with $$\angle$$ AHB. $$90^{\circ}$$

Therefore, since $$\angle$$ ABC is $$60^{\circ}$$ $$\angle$$ HAB is $$30^{\circ}$$ and AH is half of AB
$$AH = \frac{12}{2} = 6$$

In triangle AHB, from Pythagorean theorem:
$$AB^2= AH^2+BH^2$$;
$$12^2=6^2+BH^2; 144=36 + BH^2; BH=\sqrt{108}=6\sqrt{3}$$

Since we have the height and the lenght of CB, the area of the triangle is:

$$S=\frac{a*h_a}{2} = (5*6\sqrt{3})/2 = 15\sqrt{3}$$

What is the area of the triangle ABC? &nbs [#permalink] 15 Mar 2018, 15:05
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