Question

The hypotenuse of a right angled triangle is $3\sqrt{10}$ cm. If the smaller length is tripled and the longer length double, new hypotenuse will be $9\sqrt{5}$ cm.

The lengths of the triangle are 3 cm, and _____cm

Answer 1

$\Rightarrow$ Hypotenuse of triangle is $3\sqrt{10}$

$\Rightarrow$ The length of one legth of the triangle is $3$

$\therefore$ By using Pythagoras theorem,

$\Rightarrow$ $(3{)}^2+(Otherlength{)}^2=(3\sqrt{10}{)}^2$

$\therefore$ Other length $=\sqrt{(3\sqrt{10}{)}^2-(3{)}^2}$

$=\sqrt{90-9}$

$=\sqrt{81}$

$=9$

$\therefore$ Other length of the of triangle are $9cm$