If a + b : b + c : c + a = 6 : 7 : 8 and a + b + c = 14, then the valu

1.	If a + b : b + c : c + a = 6 : 7 : 8 and a + b + c = 14, then the value of c is(a) 6 (b) 7 (c) 8 (d) 14
Answer» (a) 6 Let a + b = 6k, b + c = 7k and c + a = 8k. Then 2(a + b + c) = 6k + 7k + 8k = 21k ⇒ 2 × 14 = 21k ⇒ k = \(\frac{2\times14}{21}=\frac43\) Also a + b + c = \(\frac{21k}{2}\) and a + b = 6k ⇒ c = \(\frac{21k}{2}\) - 6k = \(\frac{9}{2}k\) = \(\frac{9}{2}\times\frac43=6\)

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

Answer»

(a) 6

Let a + b = 6k, b + c = 7k and c + a = 8k.

Then 2(a + b + c) = 6k + 7k + 8k = 21k

⇒ 2 × 14 = 21k ⇒ k = \(\frac{2\times14}{21}=\frac43\)

Also a + b + c = \(\frac{21k}{2}\) and a + b = 6k

⇒ c = \(\frac{21k}{2}\) - 6k = \(\frac{9}{2}k\) = \(\frac{9}{2}\times\frac43=6\)