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The area of a triangular region with perimeter 8 [#permalink]
Expert's post 00:00

Question Stats: 57% (02:00) correct 42% (00:31) wrong based on 19 sessions
 Quantity A Quantity B The area of a triangular region with perimeter 8 8

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________ Director Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Re: The area of a triangular region with perimeter 8 [#permalink]
1
KUDOS
Carcass wrote:
 Quantity A Quantity B The area of a triangular region with perimeter 8 8

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.

[Reveal] Spoiler: OA
OA in 24h

Here let us assume the maximum length for the triangle with perimeter 8

the maximum length of the base of the triangle can be = 4 as if greater than 4 then the triangle rule does not apply.

Now calculating the area = 1/2 * base * altitude

= 1/2 * 4 * 4 = 8 but this is not possible as altitude has to be less than 4

So option B will be always greater than option A.
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Re: The area of a triangular region with perimeter 8 [#permalink]
How do you determine the maximum value of the base is 4 for the triangle rule to be valid? Like is it always p/2 and if so why? Director Joined: 20 Apr 2016
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Re: The area of a triangular region with perimeter 8 [#permalink]
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jezzsk8 wrote:
How do you determine the maximum value of the base is 4 for the triangle rule to be valid? Like is it always p/2 and if so why?

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
(A-B) < third side < (A+B)

SInce the perimeter is 8, the triangle rule to satisfy if we consider integer value is 3.

Here the base is 2 and the other two sides is 3, here it satisfy the triangle equation.

Now area = 1/2 *2 * 3 (since the maximum value of altitude < 3)

=3

But the sides can also be fraction and still the sides can be add upto = 8.

So I considered the maximum value of the base to be 4 and still it is < 8.

Hence B >A .

If you are unclear let me know.
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Re: The area of a triangular region with perimeter 8 [#permalink]
1
KUDOS
Carcass wrote:
 Quantity A Quantity B The area of a triangular region with perimeter 8 8

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.

As the area of triangle is maximum when base and height has 90 degree angle.Now three different types of triangles are possible.
1)45-45-90
2)30-60-90
3)x-y-90

case 1= sides are ; 1x-1x-under root 2
sum=3.4x=8
x=2.35
area:1/2 *2.35*2.35 =2.76

Case 2: sides are; 1x-under root 3x-2x
sum of sides =x+under root 3x+2x= 8
4.7x=8
x=1.7
area =1/2 *1.7*2.89=2.46

similarly case 3 Re: The area of a triangular region with perimeter 8   [#permalink] 23 Jun 2018, 20:20
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