Question

The perimeter of a triangle is (9 a+7b+c) Two of its sides are (3a+b+7c) and (6a+b+c)Find the third side.​
First answer=brainliest

Answer 1

Answer:

5b – 7c

Explanation:

As per the provided information in the given question, we have :

• Perimeter of the ∆ = (9a + 7b + 7c)
• Two sides are (3a + b + 7c) and (6a + b + c).

We are asked to calculate the third side.

In order to calculate the third side of the triangle, firstly we need to frame an equation. In order to do that so, we will use the formula of the perimeter of the triangle which will act as a linear equation here. Then by supposing the third side as an unknown value, we will find the third side by solving the equation. Let the third side be $\sf S_3$.

As we know that, perimeter of the triangle is sum of its all sides. So,

$\longrightarrow \small{ \sf{\quad { P = Sum \; of \; all \; sides}}}$

Here, it can be written as,

$\longrightarrow \small{ \sf{\quad { (9a + 7b + c) = (3a + b + 7c) + (6a + b+ c) + S_3}}}$

Removing the brackets in the RHS and LHS.

$\longrightarrow \small{ \sf{\quad { 9a + 7b + c = 3a + b + 7c + 6a + b+ c + S_3}}}$

Grouping the like terms in the RHS.

$\longrightarrow \small{ \sf{\quad { 9a +7b + c = 3a + 6a + b + b+ 7c + c + S_3}}}$

Performing addition of like terms in RHS.

$\longrightarrow \small{ \sf{\quad { 9a +7b + c = 9a + 2b + 8c + S_3}}}$

Now, transposing the terms from RHS to LHS.

$\longrightarrow \small{ \sf{\quad { 9a +7b + c - 9a - 2b - 8c =S_3}}}$

Grouping the like terms in LHS.

$\longrightarrow \small{ \sf{\quad { 9a - 9a +7b - 2b + c - 8c =S_3}}}$

Performing addition and subtraction of the terms in LHS.

$\longrightarrow \small{ \quad \underline{\boxed{ \textbf{\textsf{5b - 7c}} = \textbf{\textsf{S}}_\textbf{\textsf{3}}}}}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Therefore,

⠀⠀⠀⠀⠀★ Third side = 5b – 7c

Answer 2

Answer:

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Explanation:

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