The perimeter of an isosceles triangle is `59` cm. If the base is `23`cm, find the length of the equal sides.

Options

A. `16 cm`
B. `18 cm`
C. `17 cm`
D. `14 cm`

Answer

To solve the problem step by step, we will use the information given about the isosceles triangle.

### Step 1: Understand the properties of the isosceles triangle
An isosceles triangle has two equal sides. Let's denote the length of each of the equal sides as \( x \). The base of the triangle is given as \( 23 \) cm.

### 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 perimeter can be expressed as:
\[ P = x + x + \text{base} \]
Substituting the known values:
\[ P = x + x + 23 = 2x + 23 \]

### Step 3: Set up the equation using the given perimeter
We know from the problem that the perimeter is \( 59 \) cm. Therefore, we can set up the equation:
\[ 2x + 23 = 59 \]

### Step 4: Solve for \( x \)
To find \( x \), we first need to isolate it. Start by subtracting \( 23 \) from both sides of the equation:
\[ 2x = 59 - 23 \]
Calculating the right side:
\[ 2x = 36 \]

Next, divide both sides by \( 2 \):
\[ x = \frac{36}{2} = 18 \]

### Step 5: Conclusion
The length of each of the equal sides of the isosceles triangle is \( 18 \) cm.

### Final Answer:
The length of the equal sides is \( 18 \) cm.

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