Question

In a right angled triangle with sides $a$ and $b$, and hypotenuse $c$, the altitude drawn on the hypotenuse is $x$. Then which one of the following is correct?

• A. $ab=cx$
• B. $ax=bc$
• C. $bx=ac$
• D. $ab=2cx$

Answer 1

The correct option is A $ab=cx$

Area of the $△CAB=\frac{1}{2}\times AB\times AC$
Area of the $△CAB$ is also $\frac{1}{2}\times BC\times AD$
$\Rightarrow \frac{1}{2}\cdot ab=\frac{1}{2}x.c\Rightarrow ab=cx$