2
$\begingroup$

A triangle has sides $3$, $4$, and $5$. A second triangle has a perimeter of $20$. If the two triangles are similar, what is the length of the longest side of the second triangle?

The answer I got was $25/3$, but my teacher told me that was wrong. How do I get the right answer?

$\endgroup$
  • 2
    $\begingroup$ I believe that you got the correct answer, unless you have mis-stated the question. $\endgroup$ – Mohammad Zuhair Khan May 5 at 17:59
  • 1
    $\begingroup$ Check that the problem statement is correct, because if so, your answer is also correct. What did your teacher believe the answer should be? $\endgroup$ – Deepak May 5 at 18:29
2
$\begingroup$

Since the two triangles are similar, we know that $$a'=3\cdot k\qquad b'=4\cdot k\qquad c'=5\cdot k$$ Furthermore $$a'+b'+c'=(3+4+5)\cdot k=12k=20\iff k=\frac{20}{12}=\frac53$$ Therefore

$$c'=5\cdot\frac53=\frac{25}3$$

So your answer is right!

$\endgroup$
  • $\begingroup$ Nice approach. +1. It's acceptable to just take the ratio of the perimeters immediately since the proportionality of perimeters can be assumed in similar figures, but your approach may be considered more rigorous. $\endgroup$ – Deepak May 5 at 18:30

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.