The base of isosceles `Delta ABC ` is 48 cm and its area is `168 cm^(2)` . The length of one of its equal sides is

Options

A. 8 cm
B. 15 cm
C. 17 cm
D. 25 cm

Answer

To find the length of one of the equal sides of the isosceles triangle ABC, we will follow these steps:

### Step 1: Identify the given values
- Base of the triangle (BC) = 48 cm
- Area of the triangle = 168 cm²

### Step 2: Use the formula for the area of 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:
\[ 168 = \frac{1}{2} \times 48 \times \text{height} \]

### Step 3: Solve for the height
Rearranging the equation to find the height:
\[ \text{height} = \frac{168 \times 2}{48} = \frac{336}{48} = 7 \text{ cm} \]

### Step 4: Divide the base into two equal parts
Since triangle ABC is isosceles, we can divide the base BC into two equal parts:
\[ BD = DC = \frac{48}{2} = 24 \text{ cm} \]

### Step 5: Use the Pythagorean theorem
In triangle ADB, we can apply the Pythagorean theorem:
\[ AB^2 = AD^2 + BD^2 \]
Let the length of the equal sides (AB and AC) be denoted as \( x \). We know:
- \( AD \) (height) = 7 cm
- \( BD \) = 24 cm

Substituting these values into the Pythagorean theorem:
\[ x^2 = 7^2 + 24^2 \]
\[ x^2 = 49 + 576 \]
\[ x^2 = 625 \]

### Step 6: Solve for \( x \)
Taking the square root of both sides:
\[ x = \sqrt{625} = 25 \text{ cm} \]

### Final Answer
The length of one of the equal sides of the isosceles triangle ABC is **25 cm**.

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