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# Two sides of a right triangle are 12 and 13. Which of the f

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Two sides of a right triangle are 12 and 13. Which of the f [#permalink]  10 Jan 2019, 06:44
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50% (00:34) correct 50% (01:21) wrong based on 2 sessions
Two sides of a right triangle are 12 and 13. Which of the following could be the length of the third side?

A)2

B)5

C)$$\sqrt{31}$$

D)11

E)$$\sqrt{313}$$
[Reveal] Spoiler: OA
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Re: Two sides of a right triangle are 12 and 13. Which of the f [#permalink]  11 Jan 2019, 03:14
Expert's post
amorphous wrote:
Two sides of a right triangle are 12 and 13. Which of the following could be the length of the third side?

A)2

B)5

C)$$\sqrt{31}$$

D)11

E)$$\sqrt{313}$$

Let the third side be x
Since it is a right triangle, it is possible that 13 is the hypotenuse or a side..
1) 13 is hypotenuse..
$$12^2+x^2=13^2....x^2=13^2-12^2=(13-12)(13+12)=1*25=25...x=5$$
2) 13 is a side..
$$x^2=12^2+13^2=144+169=313....x=\sqrt{313}$$

Thus B and E
_________________

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Re: Two sides of a right triangle are 12 and 13. Which of the f   [#permalink] 11 Jan 2019, 03:14
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# Two sides of a right triangle are 12 and 13. Which of the f

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