The base of an isosceles triangle is 16 cm and its area is 48 `cm^(2)`. The perimeter of the triangle is

Options

A. 41 cm
B. 36 cm
C. 48 cm
D. 324 cm

Explanation

To find the perimeter of the isosceles triangle given its base and area, we can follow these steps:

### Step 1: Understand the given information
We know:
- Base (b) = 16 cm
- Area (A) = 48 cm²

### Step 2: Use the area formula for a triangle
The area of a triangle can be calculated using the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Substituting the known values:
\[ 48 = \frac{1}{2} \times 16 \times h \]

### Step 3: Solve for height (h)
Rearranging the equation to find height:
\[ 48 = 8h \]
\[ h = \frac{48}{8} = 6 \text{ cm} \]

### Step 4: Identify the lengths of the equal sides
In an isosceles triangle, the two equal sides can be found using the Pythagorean theorem. Let each equal side be denoted as \( a \). The triangle can be divided into two right triangles, where:
- One leg is \( \frac{b}{2} = \frac{16}{2} = 8 \text{ cm} \)
- The other leg is the height \( h = 6 \text{ cm} \)

Using the Pythagorean theorem:
\[ a^2 = \left(\frac{b}{2}\right)^2 + h^2 \]
Substituting the values:
\[ a^2 = 8^2 + 6^2 \]
\[ a^2 = 64 + 36 \]
\[ a^2 = 100 \]
Taking the square root:
\[ a = \sqrt{100} = 10 \text{ cm} \]

### Step 5: Calculate the perimeter
The perimeter (P) of the triangle is the sum of all its sides:
\[ P = a + a + b = 10 + 10 + 16 \]
\[ P = 36 \text{ cm} \]

### Final Answer:
The perimeter of the triangle is **36 cm**.