The perimeter of a triangle is (7x - 15) cm. The two sides are (3x - 3) cm and `(2x -2)`cm. Find the third side.

Options

A. 3x - 13
B. 2x - 10
C. 2x - 15
D. 3x - 15

Answer

To find the third side of the triangle, we can follow these steps:

### Step 1: Write down the given information
We know that:
- The perimeter of the triangle is \(7x - 15\) cm.
- The first side is \(3x - 3\) cm.
- The second side is \(2x - 2\) cm.

### Step 2: Set up the equation for the perimeter
The perimeter of a triangle is the sum of all its sides. Therefore, we can express this as:
\[ \text{Perimeter} = \text{First Side} + \text{Second Side} + \text{Third Side} \]
Let the third side be \(y\). So, we can write:
\[ 7x - 15 = (3x - 3) + (2x - 2) + y \]

### Step 3: Simplify the equation
Now, we simplify the right side:
\[ 7x - 15 = 3x - 3 + 2x - 2 + y \]
Combining like terms:
\[ 7x - 15 = (3x + 2x) + (-3 - 2) + y \]
This simplifies to:
\[ 7x - 15 = 5x - 5 + y \]

### Step 4: Isolate \(y\)
To find \(y\), we rearrange the equation:
\[ y = 7x - 15 - 5x + 5 \]
Now, combine like terms:
\[ y = (7x - 5x) + (-15 + 5) \]
This gives us:
\[ y = 2x - 10 \]

### Step 5: State the final answer
Thus, the third side of the triangle is:
\[ y = 2x - 10 \text{ cm} \]

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