Question

. For a triangle, it is given that, s – a = 3 cm, s – b = 2 cm and s – c = 1 cm. The perimeter of the triangle is :​

Answer 1

Answer:

The area of a triangle is given by

A=

s(s−a)(s−b)(s−c)

where s is the semi-perimeter, a,b,c are the sides of the triangle.

Here,

s=5,a=4

Thus,

A=

5(5−4)(5−b)(5−c)

A

2

=5(5−b)(5−c)

We also have the condition b+c=6 and so

A

2

=5(5−b)(5−6+b)

A

2

=5(5−b)(b−1)

Differentiating both sides w.r.t b, we get 0=5−b+(b−1)(−1)

⇒0=5−b+1−b

Or

b=3 and therefore, c=3