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Pop up Quiz on Triangles

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Pop up Quiz on Triangles

by aardvax » Sat Sep 04, 2010 2:22 am
Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?

I. 2

II. 12

III. 24

II only


A. II only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III.

Please post your answers, I feel that the third side should be >= 3 for making the figure pass the rule

Any side of a triangle will always be less than the sum of the other two sides but greater than the difference of the other two sides.

Can we make triangles of sides ?
8,6,1
8,6,2

i think the answer should be C here, however the explanation considered E (taking area as 0<Area<=24)
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by sanju09 » Sat Sep 04, 2010 2:51 am
aardvax wrote:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?

I. 2

II. 12

III. 24

II only


A. II only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III.

Please post your answers, I feel that the third side should be >= 3 for making the figure pass the rule

Any side of a triangle will always be less than the sum of the other two sides but greater than the difference of the other two sides.

Can we make triangles of sides ?
8,6,1
8,6,2

i think the answer should be C here, however the explanation considered E (taking area as 0<Area<=24)

The third side could measure x, such that x < 6 + 8 or x < 14, and x > 8 - 6 or x > 2; hence, x cannot take 2 or less.

2 is also a possible area as it's height could be as small as ½ for 8 as base, where 8 is one of the sides of the triangle. The maximum area of a triangle with sides 6 and 8 is 24, when the sides include right angle.

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by aardvax » Sat Sep 04, 2010 1:27 pm
thanks sanju fr the explanation.. i was just too obsessed with making one of the sides as height while calculating the area...
in 1/2 x b x h

I am clear now.... there is no need to consider the third side while calculating the min area...
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