For right triangle JKL, side KL has a length of 60 meters. If JK JL,

Question

For right triangle JKL, side KL has a length of 60 meters. If  JK > JL , which of the following could represent the lengths of sides JK and JL? Make one selection in each column.

chetan2u · Accepted Answer

Step I
Can there be any other hypotenuse other than 60.
Only choice greater than 60 is 90.
 x^2+60^2=90^2 , x also has to be multiple of 10. But 30 cannot fit in.

Step II
So 60 is the hypotenuse. 
Now we should know 2-3 types of right angled triangle. 
a)  1:\sqrt{3}:2 
b)  3:4:5 
Since we do not have any choices in  \sqrt{3} , we can skip first and check for second. 
3:4:5=x:y:60=12*3:12*4:12*5=36:48:60

JK>JL, so JK=48 and JL=36

sayan640 · Answer

MartyMurray  Can this question come in the gmat focus ?

sayan640 · Answer

chetan2u  , Can you please elaborate this as to how you came to this decision that 60 is the hypotaneuse ?

MartyMurray · Answer

I've seen at least one question that involves the Pythagorean theorem on a GMAT Focus Edition practice test. However, that question is mostly a Probability question that happens to require rather basic use of the Pythagorean theorem.

In contrast, this question is a pure Geometry question, and it requires slightly more sophisticated use of the Pythagorean theorem. So, probably, a question like this won't appear on the Focus Edition. I'm not going to 100 percent rule out the possibility that one will though.

Also, this question is definitely close to something that could appear on the Focus Edition. So, for the purposes of preparing for the Focus Edition, it's worthwhile to learn how to answer this question.

chetan2u · Answer

HYpotenuse has to be the largest side, and we know one of the side is 60, so hypotenuse has to be >60 or this side 60 itself.

90 as hypotenuse does not fit in, so KL itself must be the hypotenuse.

Robo_123 · Answer

can someone please explain this in detail?

Bunuel · Answer

We have a right triangle, and one side is 60 m.

First, 60 must be the hypotenuse, because if the hypotenuse were 90, 90^2 = 8100, and no pair of sides from the options would reach that sum.

So, x^2 + y^2 = 60^2 = 3600.
The sum must end with 0. Checking last digits:
24^2 ends with 6, 30^2 ends with 0, 36^2 ends with 6, 48^2 ends with 4.
Only pairs (24, 48) and (36, 48) can give a sum ending in 0.

Check:
 24^2 + 48^2 = 576 + 2304 = 2880
 36^2 + 48^2 = 1296 + 2304 = 3600

So, JK = 48 m and JL = 36 m.

pappal · Answer

If we don't consider KL=60 as hypotenuse then only option for hypotenuse, the greatest side is 90,which isn't correct as the leftover side will then be 30* sq.root(5)---not in the given choices
however on taking 60 as hypotenuse only choices whose squares will add up to 3600 are  36 & 48  since the square of the unit digits of these numbers add up to 100.(no need for lengthy calculations to find the squares of 36,48)

For right triangle JKL, side KL has a length of 60 meters. If JK > JL,

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JK	JL	--------
		24
		30
		36
		48
		60
		90

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