Question

$\Delta ABC$ is a right angled at A and AD is the altitude to BC. If AB = 7 cm and AC = 24 cm. Find the ratio of AD to AM, where M is the midpoint of BC:

• A. $25:41$
• B. $32:41$
• C. $\frac{336}{625}$
• D. $\frac{625}{336}$

Answer 1

The correct option is C $\frac{336}{625}$

$\because$ AM is the median of a right angled triangle.
$\therefore AM=\frac{BC}{2}=\frac{25}{2}$

and $AD=\frac{AB\times AC}{BC}=\frac{7\times 24}{25}$
$\therefore \frac{AD}{AM}=\frac{7\times 24\times 2}{25\times 25}=\frac{336}{625}$