Triangle ABC has a perimeter of 18. Which of the following cannot be

Question

Triangle ABC has a perimeter of 18. Which of the following cannot be the area of triangle ABC?

(A) 119/359
(B) 359/119
(C) π
(D) 12
(E) 16

pikolo2510 · Accepted Answer

2 rules to remember always in such questions
- For a given perimeter, equilateral triangle has the largest area
- For a given area, equilateral triangle has the smallest perimeter

With the above context, if perimeter is 18 then each side of an equilateral triangle will be 6

Area will be (sqrt)3*3*3/4=9(sqrt)3~15.3

Hence only option above 15 is E. Answer is E

jedit · Answer

It should be  E . Even if the triangle is equilateral (side 6) in which case its area would be maximum, area cannot be 16.

A*\sqrt{3}/4

6*\sqrt{3}/4   = 15.59

Rest of the values are possible by playing with large and small values of base and height.

TheGuyDangerous · Answer

Like pikolo2510 mentioned already, for a given perimeter, an equilateral triangle has the largest area.

=> Area = 1/2*6*3(1.7) ~= 15.3

=> The area cannot be greater than 15.3. => 16 is not a possible area!

Ans E

vanam52923 · Answer

Bunuel

doesnot the rule say :
for given perimeter, isosceles right angled traingle has maximum area?
which one is correct ?

Bunuel · Answer

• For a given perimeter equilateral triangle has the largest area. 
• For a given area equilateral triangle has the smallest perimeter.

Nirmesh83 · Answer

S = a+b+c/2
 = 18/2 
 =9
Area = sqrt (s)(s-a) (s-b) (s-c)
 = Sqrt 9*k
 = 3 sqrtk
Means area is factor of 3 
So ,16 can' t be the area
So Answer is E
 Bunuel  : please correct me.

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Fdambro294 · Answer

Given a constant addition of terms ———-> any product of those terms will be maximized if we make those terms equal to themselves

In this case, let the side lengths of the triangle be: A , B, C

A + B + C = 18

Given this constant addition of the three variables that sum to the triangle’s perimeter, we will maximize the product of the unknown quantities of we make them equal.

Let A = B = C = 6

The area of an equilateral triangle with side 6 is the MAX Area that this triangle can have

MAX area = (6)^2 * sqrt(3) * (1/4)

MAX area = 9 * sqrt(3) ~ 15.3 (an overestimate)

0 < Area of triangle < 15.3

This, the answer is E

Triangle can not take an area of 16

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Rokacky · Answer

The triangle will have the maximum area if it is a equilateral triangle.
Hence Option E.

Triangle ABC has a perimeter of 18. Which of the following cannot be

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GMAT Problem Solving (PS) Questions

Triangle ABC has a perimeter of 18. Which of the following cannot be

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards