If a+b : b+c : c+a = 6 : 7 : 8 and a + b + c = 14, then the value of c is : . Options :6872
Question
If a + b : b + c : c + a = 6 : 7 : 8 and a + b + c = 14, then the value of c is :
Options: 6872
Solution
The problem can be solved in the following steps:
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Given that a+b : b+c : c+a = 6 : 7 : 8, we can say that a+b, b+c, and c+a are in the ratio 6:7:8.
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We also know that a + b + c = 14.
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We can add the three ratios together to get 2(a+b+c) = 6+7+8 = 21.
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Substituting the value of a+b+c from step 2, we get 2*14 = 21.
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Solving this equation, we get the value of 1 unit = 28/21 = 4/3.
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Now, we can find the value of c by subtracting the value of a+b from the total, i.e., 14 - (6*4/3) = 14 - 8 = 6.
So, the value of c is 6.
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