The base of an isosceles triangle is 3a - 2 units and the two equal sides in 5a + 3 units. The perimeter of the triangle is

Options

A. 11a - 1 units
B. 8a + 1 units
C. 13a + 4 units
D. 4a -5 units

Answer

To find the perimeter of the isosceles triangle, we will follow these steps:

### Step 1: Identify the sides of the triangle
The base of the isosceles triangle is given as \(3a - 2\) units, and the two equal sides are given as \(5a + 3\) units each.

### Step 2: Write the formula for the perimeter
The perimeter \(P\) of a triangle is the sum of the lengths of all its sides. For our isosceles triangle, the formula will be:
\[ P = \text{Base} + \text{Side 1} + \text{Side 2} \]
Substituting the values, we have:
\[ P = (3a - 2) + (5a + 3) + (5a + 3) \]

### Step 3: Simplify the expression
Now, we will simplify the expression:
\[ P = (3a - 2) + (5a + 3) + (5a + 3) \]
Combining like terms:
- For the \(a\) terms: \(3a + 5a + 5a = 13a\)
- For the constant terms: \(-2 + 3 + 3 = 4\)

So, we can write:
\[ P = 13a + 4 \]

### Step 4: State the final answer
The perimeter of the isosceles triangle is:
\[ \boxed{13a + 4 \text{ units}} \]

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