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Is triangle ABC a right triangle? (1) The ratio of the largest to the

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Is triangle ABC a right triangle? (1) The ratio of the largest to the [#permalink]

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09 Sep 2018, 07:50

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Is triangle ABC a right triangle?

(1) The ratio of the largest to the smallest side of the triangle is 5 : 3.
(2) The ratio of the smallest side to the next larger side is 3 : 4.

Spoiler: OA

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Is triangle ABC a right triangle? (1) The ratio of the largest to the [#permalink]

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Updated on: 09 Sep 2018, 18:51

Bunuel wrote:

Is triangle ABC a right triangle?

(1) The ratio of the largest to the smallest side of the triangle is 5 : 3.
(2) The ratio of the smallest side to the next larger side is 3 : 4.

We can use the property Sum of 2 sides of a triangle should be larger than the third side

Statement 1:
This tells us that the two sides are 5 (largest) and 3(Smallest). For the third side we can take values from 3 to 6, but as the statement mentions 5 is largest and 3 is smallest. Hence, we can take values from 3 to 5 such as 3.5 or 4.5. Hence, insuff to determine if its a Right triangle.

Statement 2:
This tells us that the two sides are 3(Smallest) and 4(Second largest). For the third side we can take values from 3 to any value. Hence, insuff to determine if its a Right triangle.

Combining both we get 3:4:5 which forms a right angled triangle.

+1 for C
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Originally posted by Akash720 on 09 Sep 2018, 08:00.
Last edited by Akash720 on 09 Sep 2018, 18:51, edited 1 time in total.

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Re: Is triangle ABC a right triangle? (1) The ratio of the largest to the [#permalink]

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09 Sep 2018, 18:47

Bunuel wrote:

Is triangle ABC a right triangle?

(1) The ratio of the largest to the smallest side of the triangle is 5 : 3.
(2) The ratio of the smallest side to the next larger side is 3 : 4.

Question stem:- Is ABC a right triangle?

St1:- The ratio of the largest to the smallest side of the triangle is 5 : 3.
Note:- Ratio relationship with the third side is not given.
Length of third side lies between 3x to 5x (both 3x and 5x are exclusive)

a)Say x=1,then measure of third side=4 , so it's a right angled triangle(3,4,5)
b)Say x=1,when measure of third side=Any value between 3 to 5 (not necessarily integers, say 3.5,4.1 etc), then it's not a right angled triangle Insufficient.

St2:- The ratio of the smallest side to the next larger side is 3 : 4
As per triangle inequality theorem, the measure of third side can be any number less than 7x(=3x+4x) and greater than x(=4x-3x).

say x=1, then the sides of the triangle would be 3,4, and 1<3rd side<7.
Insufficient.

Combined,
Sides of the triangle are in the ration 3k:4k:5k.

So, the triangle ABC is a right angled triangle.

Ans. (C)
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