1
$\begingroup$

Given a right triangle whose side lengths are all integer multiples of 8, how many units are in the smallest possible perimeter of such a triangle?

Does this mean the side lengths and not the hypotenuse or does it mean all three sides?

$\endgroup$
  • $\begingroup$ All three sides, dear… $\endgroup$ – Parcly Taxel Feb 24 '18 at 3:36
  • $\begingroup$ So if they're all integer multiples of 8, then the sides would have to be 24, 32, and 40. So P=96. $\endgroup$ – ddswsd Feb 24 '18 at 3:38
3
$\begingroup$

We have $$(8a)^2+(8b)^2=(8c)^2$$ Dividing by 64: $$a^2+b^2=c^2$$ As is well-known, the smallest possible integer values for these variables are $a=3,b=4,c=5$, so the smallest possible perimeter is $$8(a+b+c)=8\cdot12=96$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.