Question

If in ΔABC, `sin  "B"/2 sin  "C"/2 = sin  "A"/2` and 2s is the perimeter of the triangle, then s is ______.

Options

• a

• 2a

• 3a

• 4a

Answer 1

If in ΔABC, `sin  "B"/2 sin  "C"/2 = sin  "A"/2` and 2s is the perimeter of the triangle, then s is 2a.

Explanation:

Given, `sin  "B"/2 sin  "C"/2 = sin  "A"/2` 

⇒ `sqrt((("s" - "a")("s" - "c"))/"ac") xx sqrt((("s" - "a")("s" - "b"))/"ab") = sqrt((("s" - "b")("s" - "c"))/"bc")`

⇒ `(("s" - "a"))/"a" sqrt((("s" - "b")("s" - "c"))/"bc") = sqrt((("s" - "b")("s" - "c"))/"bc")` 

⇒ s – a = a

⇒ s = 2a