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mathematics

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by [email protected] » Sun Oct 01, 2017 10:16 am
Hi Diophantus,

One of the right-triangle 'patterns' that you will likely see on the GMAT is the 5/12/13. It's important to remember that MULTIPLES of this ratio are also valid right triangles. Thus, you could have sides of...
5, 12 and 13
10, 24 and 26
15, 36 and 39
Etc.

Here, we know that the hypotenuse is 39 and the ratio of the two 'legs' is 5:12. Thus, those two legs must be...

15 and 36

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by Jay@ManhattanReview » Sun Oct 01, 2017 9:14 pm
Diophantus wrote:In a right-angled triangle, the hypotenuse is 39cm and the ratio of the other two sides is 12:5. Find the sides
Diophantus wrote:In a right-angled triangle, the hypotenuse is 39cm and the ratio of the other two sides is 12:5. Find the sides
Which side do you want? there are two sides...

Say one of the sides is 12x and thus, the other one is 5x.

Thus, applying Pythagoras theorem, we get,

39^2 = (12x)^2 + (5x)^2

39^2 = 144x^2 + 25x^2

39^2 = 169x^2

Taking square root of both sides, we get

39 = 13x => x = 3

Thus, the two sides are 12*3 = 36 cm and 5*3 = 15 cm.

Pl. post a question with five options and the answer.

Hope this helps!

-Jay

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