Question

If a+b:b+c:c+a=6:7:8 and a+b+c=14 then value of c​

Answer 1

Answer: c = 6

Step-by-step explanation:

Let a + b = 6x , b + c = 7x , c + a = 8x respectively .

Then (a + b) + (b + c) + (c + a) = 6x + 7x + 8x

⇒ 2a + 2b + 2c = 21x

⇒ 2(a + b + c) = 21x

⇒ 2 * 14 = 21x

⇒ x = (2 * 14)/21

⇒ x = 4/3

Therefore a + b = 6x = 6 * 4/3 = 24/3

b + c = 7x = 7 * 4/3 = 28/3

c + a = 8x = 8 * 4/3 = 32/3

Subtracting (a + b) from (b + c) , we get -

(b + c) - (a + b) = 4/3

⇒ c - a = 4/3

Also c + a = 32/3

Adding (c - a) and (c + a) , we get -

(c - a) + (c + a) = 36/3 = 12

⇒ 2c = 12

⇒ c = 6