Question

In right angle $\Delta ABC,AB=a,AC=b,BC=c$ and $CD$ is ${\perp }^r$ on AB. Find the value $x=CD$.

• A. $\frac{ab}{c}$
• B. $\frac{c}{ab}$
• C. $\frac{bc}{a}$
• D. $\frac{ac}{b}$

Answer 1

The correct option is C $\frac{bc}{a}$

Given right angle triangle $ABC,AB=aAC=b$ and $CD$ is perpendicular to $AB$

Then area of $\Delta ABC=\frac{1}{2}AC\times BC=\frac{1}{2}\times b\times c=\frac{1}{2}bc$

Also, area of $\Delta ABC=\frac{1}{2}AB\times CD=\frac{1}{2}\times a\times x=\frac{1}{2}xa$

$\therefore \frac{1}{2}bc=\frac{1}{2}xa$

$\Rightarrow xa=bc$

$\Rightarrow x=\frac{bc}{a}$