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
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 $a^2$.