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If (a + b) : (b + c) : (c + a) and (a + b + c) = 14, then the value of c is = ?

16
27
38
414

Answer:- 1

Explanation:-

Solution:

(a + b) : (b + c) : (c + a)
6 : 7 : 8
Le t 6x : 7x : 8x
∴ a + b + b + c + a = 6x + 7x + 8x

\begin{aligned} \Rightarrow 2 a + 2 b + 2 c = 21 x \\ \Rightarrow 2 (a + b + c) = 21 x \\ \Rightarrow a + b + c = \frac{21}{2} x \\ \Rightarrow a + b + c = 14 given \\ \Rightarrow \frac{21 x}{2} = 14 \\ \Rightarrow x = \frac{28}{21} = \frac{4}{3} \\ ∴ a + b = 6 \times \frac{4}{3} = 8 \\ ∴ a + b + c = 14 \\ \Rightarrow 8 + c = 14 \\ \Rightarrow c = 14 - 8 = 6 \end{aligned}

$\eqalign{ & \Rightarrow 2a + 2b + 2c = 21x \cr & \Rightarrow 2\left( {a + b + c} \right) = 21x \cr & \Rightarrow a + b + c = \frac{{21}}{2}x \cr & \Rightarrow a + b + c = 14{\text{ given}} \cr & \Rightarrow \frac{{21x}}{2} = 14 \cr & \Rightarrow x = \frac{{28}}{{21}} = \frac{4}{3} \cr & \therefore a + b = 6 \times \frac{4}{3} = 8 \cr & \therefore a + b + c = 14 \cr & \Rightarrow 8 + c = 14 \cr & \Rightarrow c = 14 - 8 = 6 \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

(a + b) : (b + c) : (c + a)
6 : 7 : 8
Le t 6x : 7x : 8x
∴ a + b + b + c + a = 6x + 7x + 8x

\begin{aligned} \Rightarrow 2 a + 2 b + 2 c = 21 x \\ \Rightarrow 2 (a + b + c) = 21 x \\ \Rightarrow a + b + c = \frac{21}{2} x \\ \Rightarrow a + b + c = 14 given \\ \Rightarrow \frac{21 x}{2} = 14 \\ \Rightarrow x = \frac{28}{21} = \frac{4}{3} \\ ∴ a + b = 6 \times \frac{4}{3} = 8 \\ ∴ a + b + c = 14 \\ \Rightarrow 8 + c = 14 \\ \Rightarrow c = 14 - 8 = 6 \end{aligned}

$\eqalign{ & \Rightarrow 2a + 2b + 2c = 21x \cr & \Rightarrow 2\left( {a + b + c} \right) = 21x \cr & \Rightarrow a + b + c = \frac{{21}}{2}x \cr & \Rightarrow a + b + c = 14{\text{ given}} \cr & \Rightarrow \frac{{21x}}{2} = 14 \cr & \Rightarrow x = \frac{{28}}{{21}} = \frac{4}{3} \cr & \therefore a + b = 6 \times \frac{4}{3} = 8 \cr & \therefore a + b + c = 14 \cr & \Rightarrow 8 + c = 14 \cr & \Rightarrow c = 14 - 8 = 6 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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