Question

In `Delta ABC`, angle A is `120^(@), BC + CA = 20, and AB + BC = 21` Find the length of the side BC

Answer 1

Correct Answer - 13 units
Given `a + b = 20 and c + a = 21`
Now, `a^(2) = b^(2) + c^(2) - 2bc cos (120^(@))`
`rArr a^(2) = (20 -a)^(2) + (21 -a)^(2) + (2(20 -a) (21 -a))/(2)`
or `2a^(2) - 123a + 1261 = 0`
or `2a^(2) - 26a - 97 a + 1261 = 0`
or `2a (a - 13) - 97 (a - 13) = 0`
or `a = 13, 97//2`
`:. a = 13 " " [" as " a = 97//2 " is not possible"]`