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"The base of an isosceles triangle is 16 cm and its area is 48 cm². Then the perimeter of the triangle is:"

Let's solve this step by step:

### Step 1: Define Variables
Let the height of the isosceles triangle be \( h \), and let the two equal sides of the triangle be \( a \).

The area \( A \) of the triangle is given by the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
Given:
- Base = 16 cm
- Area = 48 cm²

### Step 2: Calculate the Height
Using the area formula:
\[
48 = \frac{1}{2} \times 16 \times h
\]
Solving for \( h \):
\[
48 = 8 \times h
\]
\[
h = \frac{48}{8} = 6 \, \text{cm}
\]

### Step 3: Use the Pythagorean Theorem to Find the Length of the Equal Sides
Since the triangle is isosceles, the height splits the triangle into two right triangles with:
- One leg as half of the base (8 cm),
- The other leg as the height (6 cm),
- Hypotenuse as one of the equal sides \( a \).

Using the Pythagorean theorem:
\[
a^2 = 8^2 + 6^2
\]
\[
a^2 = 64 + 36 = 100
\]
\[
a = \sqrt{100} = 10 \, \text{cm}
\]

### Step 4: Calculate the Perimeter
The perimeter \( P \) of the isosceles triangle is given by:
\[
P = \text{base} + 2 \times \text{equal side}
\]
\[
P = 16 + 2 \times 10 = 16 + 20 = 36 \, \text{cm}
\]

### Final Answer:
The perimeter of the triangle is \( \boxed{36} \) cm.

Would you like more details or further explanations?

Here are some related questions for practice:
1. How do you calculate the area of any triangle given the base and height?
2. How does the Pythagorean theorem apply to isosceles triangles?
3. What is the relationship between the height and equal sides of an isosceles triangle?
4. How do you find the perimeter of other types of triangles?
5. What other properties distinguish isosceles triangles from other types?

**Tip:** Remember that in any isosceles triangle, the altitude from the vertex to the base bisects the base into two equal segments, creating two right triangles.

The base of an isosceles triangle is 16 cm and its area is 48 cm². Then the perimeter of the triangle is:

Find the perimeter of an isosceles triangle with a base of 16 cm and area of 48 cm². This problem involves using the area formula and the Pythagorean theorem to solve for the length of the equal sides and calculate the perimeter. Suitable for students in Grades 6-8.

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