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

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Bunuel
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Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post  20 Jul 2017, 21:38
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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
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Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post  28 Jul 2017, 08:19
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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
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Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post  21 Jul 2017, 00:49
Bunuel wrote:
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


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.
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Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post  Updated on: 22 Nov 2019, 03:12
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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

Originally posted by TheGuyDangerous on 22 Nov 2019, 02:55.
Last edited by TheGuyDangerous on 22 Nov 2019, 03:12, edited 1 time in total.
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vanam52923
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Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post  22 Nov 2019, 03:10
pikolo2510 wrote:
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


Bunuel

doesnot the rule say :
for given perimeter, isosceles right angled traingle has maximum area?
which one is correct ?
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Bunuel
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Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post  22 Nov 2019, 03:14
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vanam52923 wrote:
pikolo2510 wrote:
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


Bunuel

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


• For a given perimeter equilateral triangle has the largest area.
• For a given area equilateral triangle has the smallest perimeter.
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Nirmesh83
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Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post  24 Sep 2021, 07:27
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
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Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post  10 Oct 2021, 18:50
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
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Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post  11 Oct 2021, 00:10
The triangle will have the maximum area if it is a equilateral triangle.
Hence Option E.
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Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink]
11 Oct 2021, 00:10
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