Question

The hypotenuse of a right triangle is $3\sqrt{10}\mathrm{cm}$. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be $9\sqrt{5}\mathrm{cm}$. How long are the legs of the triangle?

Answer 1

Let the length of smaller side of right triangle be then larger side be

Then, as we know that by Pythagoras theorem

….. (1)

If the smaller side is triple and the larger side be doubled, the new hypotenuse is

Therefore,

….. (2)

From equation (1) we get

Now putting the value of in equation (2)

But, the side of right triangle can never be negative

Therefore, when then

Hence, length of smaller side of right triangle be then larger side be