Question

The perimeter of a triangle is $60m$ and its sides are in the ratio $5:12:13$, find the length of the altitude of the triangle corresponding to the longest side

• A. $9\frac{3}{13}m$
• B. $5\frac{4}{12}m$
• C. $6\frac{9}{11}m$
• D. $7\frac{2}{15}m$

Answer 1

Answer: (A)

$9\frac{3}{13}m$

Perimeter of triangle = $60m$ & sides are in ratio $5:12:13$

$\Rightarrow 5x+12x+13x=60\Rightarrow x=2$

$\therefore$ Sides are $10,24,26m$.

From $\Delta ABD$ & $\Delta ADC$

$A{D}^2={10}^2-x^2={24}^2-(26-x{)}^2$

$\Rightarrow 100-x^2=576-676-x^2+52x$

$\Rightarrow x=3.846$

$\therefore A{D}^2={10}^2-(3-846{)}^2\Rightarrow AD=9.23=9\frac{3}{13}m$