Question

Question 9
Write True or False and justify your answer:

In a triangle, the sides are given as 11cm, 12cm and 13cm. the length of the altitude is 10.25 cm corresponding to the side having 12 cm.

Answer 1

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