Question

In a triangle $ABC$, $\angle BAC={90}^{\circ };$ $AD$ is the altitude from $A$ on to $BC.$ Draw $DE$ perpendicular to $AC$ and $DF$ perpendicular to $AB.$ Suppose $AB=15$ and $BC=25.$ Then the length of $EF$ is

• A. $12$
• B. $10$
• C. $5\sqrt{3}$
• D. $5\sqrt{5}$

Answer 1

The correct option is A $12$

Here given that $AB=15,BC=25\Rightarrow AC=20$

$\text{Now,}2\times \text{Area of}\Delta ABC=AD\times BC=AB\times AC$
$\Rightarrow AD=12$

From the figure, $EDFA$ is a rectangle.
Since diagonals of a rectangle are equal,
$AD=EF=12$