Question

If (a+b):(b+c):(c+a)=6:7:8 and a+b+c=14, then find a:b:c and the value of a, b and c

Answer 1

Answer:

a:b:c = (4.66):(3.33):6

a = 4.66

b = 3.33

c = 6

Step-by-step explanation:

Since it is ratios we have to assume it as

6k, 7k, 8k

a+b = 6k

b+c = 7k

c+a = 8k

Adding the above, we get

2a+2b+2c = 21k ----- 1

a+b+c = 14

∴ a + b = 14 - c

Substituting the value in 1

2a + 2b + 2c = 21k

2(a + b) + 2c = 21k

2(14 - c) + 2c = 21k

28 - 2c + 2c = 21k

28 = 21k

28/21 = k

a + b = 6k

14 - c = 6(28/21)

14 - c = 168/21

14 - c = 8

-c = 8 - 14

-c = -6

∴ c = 6

b + c = 7k

b + 6 = 7(28/21)

b + 6 = 9.33

b = 9.33 - 6

∴ b = 3.33

c + a = 8k

6 + a = 8(28/21)

6 + a = 10.66

a = 10.66 - 6

∴ a = 4.66

a:b:c = (4.66):(3.33):6

a = 4.66

b = 3.33

c = 6