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Is the area of the triangle ABC more than 12 sq. units?

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Is the area of the triangle ABC more than 12 sq. units?

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Is the area of the triangle ABC more than 12 sq. units?

(1) The GCD of the sides AB and AC is 2.
(2) The LCM of the sides AB and AC is 12.

The OA is C.

I would like to knwo how to solve this DS question. Any expert can help me here? Please.

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Vincen wrote:
Is the area of the triangle ABC more than 12 sq. units?

(1) The GCD of the sides AB and AC is 2.
(2) The LCM of the sides AB and AC is 12.

The OA is C.

I would like to knwo how to solve this DS question. Any expert can help me here? Please.
(1) The GCD of the sides AB and AC is 2.

Case 1: If AB = 2 and AC = 2 and ABC is a rightangled triangle, then the area of the triangle ABC = (1/2)*AB*AC= 1/2*2*2 = 2 < 12.
Case 2: If AB = 3 and AC = 10 and ABC is a rightangled triangle, then the area of the triangle ABC = (1/2)*AB*AC= 1/2*6*10 = 30 > 12. No unique answer. Insufficient.

(2) The LCM of the sides AB and AC is 12.

Case 1: If AB = 3 and AC = 4 and ABC is a rightangled triangle, then the area of the triangle ABC = (1/2)*AB*AC= 1/2*3*4 = 6 < 12.
Case 2: If AB = 3 and AC = 12 and ABC is a rightangled triangle, then the area of the triangle ABC = (1/2)*AB*AC= 1/2*6*12 = 36 > 12. No unique answer. Insufficient.

(1) and (2) together

Since GCD = 2 and LCM = 12, we have AB*AC = 2*12 = 24.

The maximum possible area of the triangle ABC = (1/2)*AB*AC= 1/2*24 = 12 (Not greater than 12). Sufficient.

The correct answer: C

Hope this helps!

-Jay
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