Question

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

• A. $10\text{cm}$
• B. $10.25\text{cm}$
• C. $10.5\text{cm}$
• D. $10.75\text{cm}$

Answer 1

The correct option is B $10.25\text{cm}$

Given, the sides of a triangle are:
a = 11 cm, b = 12 cm and c = 13 cm.
Now, semi-perimeter,
$s=\frac{a+b+c}{2}$
$=\frac{11+12+13}{2}=\frac{36}{2}=18\text{cm}$
Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$ [by Heron’s formula]
$=\sqrt{18(18-11)(18-12)(18-13)}$
$=\sqrt{18\times 7\times 6\times 5}$
$=\sqrt{3\times 6\times 7\times 6\times 5}$
$=6\sqrt{3\times 7\times 5}$
$=6\sqrt{105}=6\times 10.25$
$=61.5c{m}^2$
$\therefore \text{Area of}\Delta ABC=\frac{1}{2}\times BC\times AD$
$[\because areaoftriangle=\frac{1}{2}(base\times height\left)\right]$
$61.5=\frac{1}{2}\times 12\times AD⟹AD=10.25\text{cm}$