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So here's the question :

The hypotenuse of a right triangle is $3 \sqrt 5$ cm. If the smaller side is tripled & the larger side is doubled, the new hypotenuse will be $15$ cm. Find the length of each side.

Need the answer with steps please.

Regards,
Netizen

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    $\sqrt{a^2+b^2}=3\sqrt{5}$ and $\sqrt{(3a)^2+(2b)^2}=15$. A problem with the way you phrase your question is that it looks as if you're passing on to us a question that someone else wrote rather than asking your own question, so it's as if you're doing stenography.2011-12-20

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For the smaller triangle you have $ \sqrt{a^2+b^2} = 3\sqrt{5}, $ so $ a^2+b^2 = 3^2\cdot 5 = 45.\tag{1} $ For the larger triangle you need $ \sqrt{(3a)^2+(2b)^2} = 15, $ so $ 9a^2+4b^2 = 15^2 = 225.\tag{2} $ If you say $a^2=45-b^2$, and consequently put $45-b^2$ in place of $a^2$ in (2), then it's easy to solve that for $b^2$, and then put that solution for $b^2$ into $45-b^2$ to find $a^2$.

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    Thanks a lot ! You made my day !2011-12-20