Geometry + DS

[harsh.champ]

What is the length of the side AB of triangle ABC?

(X) AB <= AC = 2, and area of triangle ABC is 2
(Y) Exactly two sides have integer length

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Seeking advice regarding the problem approach!!

[Mom4MBA]

I think the answer is E

[November Rain]

Hi,

I'm not sure about this question but.... couldn't it be C?

With statement 1 and 2 the only triangle i can think of is an isosceles triangle with angles 45-45-90 wich would mean that AB = AC = 2 and BC = square root of 2.

[harsh.champ]

Hi,

I'm not sure about this question but.... couldn't it be C?

With statement 1 and 2 the only triangle i can think of is an isosceles triangle with angles 45-45-90 wich would mean that AB = AC = 2 and BC = square root of 2.

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Hi November Rain,
If we consider it to be an isosceles right angled triangle ,taking AB=AC=2,we get the hypotenuse BC as (2*root2) not (root2).I guess,you missed out on that part.

[sanju09]

Hi,

I'm not sure about this question but.... couldn't it be C?

With statement 1 and 2 the only triangle i can think of is an isosceles triangle with angles 45-45-90 wich would mean that AB = AC = 2 and BC = square root of 2.

_______________
Hi November Rain,
If we consider it to be an isosceles right angled triangle ,taking AB=AC=2,we get the hypotenuse BC as (2*root2) not (root2).I guess,you missed out on that part.

Yes, but November Rain has still made a very good point. If we take the two statements together, there's no possibility other than that, AB = 2.

[spoiler]½ * 2 * 2 = 2[/spoiler].

[spoiler]C[/spoiler]

[November Rain]

Hi sanju09,

Well, to be honest, when i took another look at the question... I started having second thoughts. Why couldn't be just A?

If we counsider that AC is the base and it's equal to 2, then the height needs to be 2 as well.

Now, either AB is the height and therefore its 2, or it is higher than the height (because otherwise it can't be a triangle). Since statement 1 tell us that AB <= 2, then AB has to be 2.


What's the OA? Does anyone know?

[sanju09]

Hi sanju09,

Well, to be honest, when i took another look at the question... I started having second thoughts. Why couldn't be just A?

If we counsider that AC is the base and it's equal to 2, then the height needs to be 2 as well.

Now, either AB is the height and therefore its 2, or it is higher than the height (because otherwise it can't be a triangle). Since statement 1 tell us that AB <= 2, then AB has to be 2.


What's the OA? Does anyone know?

oh yes