Question

Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.

Answer 1

Let the third side of the triangle be x. 
Perimeter of the given triangle = 42 cm 
18 cm + 10 cm + x = 42 x 
= 14 cm

Perimeter
s =\( \frac{\text{(a + b + c)}}{2}\)
\(= \frac{42}{2} \)
= 21 cm
By Heron’s formula,
Area of a triangle \( = \sqrt{\text{s(s - a)(s - b)(s - c)}}\)

\(= \sqrt{\text{21(21 - 18)(21 - 10)(21 - 14)}}\)

\(= \sqrt{\text{21 × 3 × 11 × 7}}\)

\(= 21\sqrt{11}\) cm²

Area of the triangle \(= 21\sqrt{11}\) cm².