Question

In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude corresponding to the side having length 12 cm is

• A. 10.25 cm
• B. 11.25 cm
• C. 12.25 cm
• D. 9.25 cm

Answer 1

Answer: (A)

10.25 cm

Sides of triangle are $11,12,13$
Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$
$s=\frac{a+b+c}{2}$
$s=\frac{11+12+13}{2}$
$s=18$
Area of triangle = $\sqrt{18\left(7\right)\left(6\right)\left(5\right)}$
Area of triangle = $\sqrt{18\left(7\right)\left(6\right)\left(5\right)}=61.5$
Area of triangle = $\frac{1}{2}\left(base\right)\left(altitude\right)$
61.5 = $\frac{1}{2}\times 12\times \left(altitude\right)$
Altitude = $10.25$