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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.


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"Need the answer with steps asap." Sounds like homework is due soon! If this is homework, please add the homework tag. –  Dilip Sarwate Dec 20 '11 at 17:59
Yup this is homework, but the previous one wasn't. –  Netizen110 Dec 20 '11 at 18:04
$\sqrt{a^2+b^2}=3\sqrt{5}$ 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. –  Michael Hardy Dec 20 '11 at 18:16
If instead of "asap", you write "please", your post would be greatly improved. –  Álvaro Lozano-Robledo Dec 20 '11 at 18:18

1 Answer 1

up vote 1 down vote accepted

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 ! –  Netizen110 Dec 20 '11 at 18:47

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