Question

If the sides of a triangle are in the ratio 5:7:8 and the in-radius of the triangle is 4 cm, then the length of the altitude corresponding to the largest side is

• A. 5
• B. 12
• C. 10
• D. 20

Answer 1

The correct option is C 10

Let the sides of the triangle are $a,b,c$, then $\frac{a}{5}=\frac{b}{7}=\frac{c}{8}=k$

$s=\frac{5k+7k+8k}{2}=10k$

$r=\frac{\Delta }{s}⟹\Delta =r\times s=40k$

Also, $\Delta =\frac{1}{2}\times 8k\times Altitude⟹Altitude=40k\times \frac{1}{4k}=10cm$