Question

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

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

`s = "Perimeter"/2=42/2=21cm`

By Heron's formula,

`"Area of a triangle "=sqrt(s(s-a)(s-b)(s-c))`

`"Area of the given triangle "=(sqrt(21(21-18)(21-10)(21-14)))cm^2`

                                         `=(sqrt(21(3)(11)(7)))cm^2`

                                        `= 21sqrt11 cm^2`