A banner is in the shape of an isosceles triangle. It has a perimeter of 7m. If the non-equal side is 2 m, find the length of the equal sides.

Answer

To find the length of the equal sides of the isosceles triangle, we can follow these steps:

### Step 1: Understand the properties of the isosceles triangle
An isosceles triangle has two equal sides and one non-equal side. In this case, the non-equal side (let's call it \( b \)) is given as 2 meters.

### Step 2: Write down the formula for the perimeter of an isosceles triangle
The perimeter \( P \) of an isosceles triangle can be expressed as:
\[ P = 2a + b \]
where \( a \) is the length of the equal sides and \( b \) is the length of the non-equal side.

### Step 3: Substitute the known values into the perimeter formula
We know the perimeter is 7 meters and the non-equal side \( b \) is 2 meters. Therefore, we can substitute these values into the formula:
\[ 7 = 2a + 2 \]

### Step 4: Solve for \( a \)
To find \( a \), we first isolate \( 2a \) by subtracting \( 2 \) from both sides:
\[ 7 - 2 = 2a \]
\[ 5 = 2a \]

Next, divide both sides by 2 to solve for \( a \):
\[ a = \frac{5}{2} \]
\[ a = 2.5 \text{ meters} \]

### Step 5: Conclusion
The length of the equal sides of the isosceles triangle is 2.5 meters.

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