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Consider a triangle with sides 9cm, 16cm and x cm. How many

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Consider a triangle with sides 9cm, 16cm and x cm. How many [#permalink]

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Consider a triangle with sides 9cm, 16cm and x cm. How many such triangles exist?

(1) The triangle is obtuse angled triangle
(2) x is an integer
[Reveal] Spoiler: OA

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Consider a triangle with sides 9cm, 16cm and x cm. How many [#permalink]

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Sasindran wrote:
Consider a triangle with sides 9cm, 16cm and x cm. How many such triangles exist?

(1) The triangle is obtuse angled triangle
(2) x is an integer


Sum of any two sides of a triangle is always greater than the other side, while the difference of any two sides is always lesser than the third side. So if three sides of a triangle are 9, 16, and x cm respectively: then x is lesser than the sum (9+16) and x is greater than the difference (16-9). So x is greater than 7 and less than 25.
7 < x < 25.

Additionally, let the three sides be a, b, c and c be the longest side.
If a^2 + b^2 > c^2 then the given triangle is an Acute angle triangle (all angles are less than 90 degree)
If a^2 + b^2 = c^2 then the given triangle is a Right angle triangle (one angle is equal to 90 degree)
If a^2 + b^2 < c^2 then the given triangle is an Obtuse angle triangle (one angle is greater than 90 degree)

(1) Given triangle is Obtuse. But we dont know if the longest side is 16 cm or the longest side is x cm. We CAN take both cases and solve, but their will be infinite cases possible because x is not necessarily an integer. x can take decimal values also (eg, 15.9, 20.2 etc). So Insufficient.

(2) We already know that 7 < x < 25, and now x is an integer. Between 7 and 25 there are 17 integers. So x can take 17 values, thus 17 different triangles are possible. Sufficient.

I personally believe answer should be B, not C (but OA is C) - as second statement alone is sufficient to answer the question. Of course, if we combine the data from first statement also, then with additional constraints, the number of possible triangles will decrease. But we dont need to combine because second statement alone is giving us a unique answer. May be experts can help. (Chetan, Karishma, Bunuel)
Consider a triangle with sides 9cm, 16cm and x cm. How many   [#permalink] 16 Jan 2018, 22:12
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