Question

In a triangle $ABC$, $BC=5cm,AC=12cm$ and $AB=13cm$. then what is the length of altitude drawn from B on AC ?

• A. $4cm$
• B. $5cm$
• C. $6cm$
• D. $7cm$

Answer 1

Answer: (B)

$5cm$

Since $5^2+{12}^2={13}^2$, the triangle is a right angled triangle with base $BC=5cm,$ and height $AC=12cm$
Area of triangle $=\frac{1}{2}\times$ base $\times$ height $=\frac{1}{2}\times 5\times 12=30$ sq cm
Area of triangle remains same, if we consider any of the base and its corresponding height to calculate it.
So, if the altitude drawn from $B$ to $AC$ is $BD$, then $\frac{1}{2}\times 12\times BD=30$ sq cm
$\therefore BD=5cm$