Question

A right angled triangle has a base of $40cm$, height of $30cm$ and hypotenuse of $50cm$. The triangle is rotated so that the hypotenuse forms the base. Find the altitude now.

Answer 1

$a=\sqrt{9-l^2}$ $b=\sqrt{16-l^2}$

$\Rightarrow a+b=5$

$a=5-b$

$a^2=25+b^2-l^2-10b$

$9-l^2=25+16-l^2-10\sqrt{16-l^2}$

$10\sqrt{16-l^2}=32$

$\sqrt{16-l^2}=3.2$

$16-l^2=10.24$

$l^2=5.76$

$\Rightarrow l=2.4cm$

Hence, the answer is $2.4cm.$