Question

Question 3
The sides of a triangle are 56m, 60cm and 52cm long. The area of the triangle is

Answer 1

Since, the three sides of a triangle are a = 56cm, b = 60cm and c = 52 cm.
Then, semi-perimeter of a triangle,
$s=\frac{a+b+c}{2}=\frac{56+60+52}{2}=\frac{168}{2}=84cm$
Area of a triangle $=\sqrt{s(s-a)(s-b)(s-c)}$ [by Heron’s formula]
$=\sqrt{84(84-56)(84-60)(84-52)}$
$=\sqrt{84\times 28\times 24\times 32}$
$=\sqrt{4\times 7\times 3\times 4\times 7\times 4\times 2\times 3\times 4\times 4\times 2}$
$=\sqrt{(4{)}^6\times (7{)}^2\times (3{)}^2}$
$=(4{)}^3\times 7\times 3=1344c{m}^2$
Hence, the area of triangle is 1344 $c{m}^2$.