Hi Turkish,

This question is based on a specific Geometry rule: When given 2 sides of a triangle, the MAXIMUM area will occur when the two sides are the LEGS of a RIGHT triangle.

So, with legs of 3 and 6, the Pythagorean Theorem will help us figure out the third side (the hypotenuse):

3^2 + 6^2 = C^2
9 + 36 = 45
45 = C^2
(Root45) = C

(Root45) = 3(Root5)

Thus, the perimeter of the triangle is 3+6+3(Root5) = 9 + 3(Root5)

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Let's consider the diagram below to find out the maximum possible area of a triangle with two of the sides given



We are given length of two sides BC = b and AC = a. We know that area of triangle = \(\frac{1}{2}\) * base * height = \(\frac{1}{2}\) * b * AD

Since we know the lengths of two sides as a and b, we need to express AD in terms of 'a' as 'b' is already present in the expression of the area.

We see that triangle ADC is a right angled triangle, so we can express AD in terms of 'a' using the trigonometric ratios.

We can write Sin ∠ACD = AD/a which gives us AD = a * Sin ∠ACD.

Hence, area of triangle ABC = \(\frac{1}{2}\) * b * a * Sin ∠ACD. This expression would be maximum when Sin ∠ACD is maximum which is when angle ∠ACD = 90 and Sin ∠ACD = 1.

Thus, it tells us that sides AC and BC are perpendicular to each other and hence form the two legs of a right angled triangle.


For two sides given the maximum area would be if these two sides form the legs of a right angled triangle


Coming back to the question, the sides given to us are 6 and 3 and we need to find the perimeter of the this right angled triangle with 6 & 3 being the legs of the right angled triangle. Using the phythagoras theorem we can calculate the hypotenuse which is the third side as 3√5.

Thus the perimeter will be 6+3+3√5 = 9 + 3√5

Answer is option D

Hope it helps

Regards
Harsh
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d) 15.7082039325
You can use TrianCal (online triangle calculator) to see value and draw it:
put 2 sides and select maximun in the area popup.

Hi JesusSD,

Since you're not going to have access to a calculator while you work through the Quant section of the GMAT, you really should NOT be using one during your practice. The ability to do basic arithmetic, by hand, is part of what is required to score at a high level on Test Day. If you're not practicing those skills now, then you won't be prepared to do the necessary work correctly (or efficiently) on Test Day.

GMAT assassins aren't born, they're made,
Rich
_________________

The whole maximum area thing through me for a loop. Didn't need to actually make use of it too much.

If two of the sides are 6 and 3, then it's clear that to maximize the area 6 has to be the base or height.

c^2 = a^2 + b^2 ---> c =3√5

3√5 + 3 + 6 = 9 + 3√5

Answer is D
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