Question

Find the value of $BD\times DC$ ,if $AD=5cm$.

• A. $25c{m}^2$
• B. $10c{m}^2$
• C. $12c{m}^2$
• D. $15c{m}^2$

Answer 1

The correct option is A $25c{m}^2$


Perpendicular from right angle to hypotenuse divides the triangle into two similar triangles and these are similar to the whole triangle also.

$△ABC\sim △DBA$

and $△ABC\sim △DAC$

$\therefore DBA\sim DAC$

$\Rightarrow \frac{AD}{CD}=\frac{DB}{DA}$

$\Rightarrow BD\times DC={AD}^2$

$\Rightarrow BD\times DC=5^2=25c{m}^2$