The base of an isosceles `DeltaABC` is 48 cm and its area is `168cm^(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 can follow these steps:

### Step 1: Understand the given information
We have an isosceles triangle ABC where:
- The base BC = 48 cm
- The area of triangle ABC = 168 cm²

### Step 2: Use the area formula for triangles
The area of a triangle can be calculated using the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
In our case, the base BC is 48 cm, and we need to find the height AD.

### Step 3: Set up the equation for the area
Substituting the known values into the area formula:
\[ 168 = \frac{1}{2} \times 48 \times AD \]

### Step 4: Solve for the height (AD)
Multiply both sides by 2 to eliminate the fraction:
\[ 336 = 48 \times AD \]
Now, divide both sides by 48:
\[ AD = \frac{336}{48} = 7 \text{ cm} \]

### Step 5: Find the lengths of segments BD and DC
Since AD is the height and it bisects the base BC in an isosceles triangle, we have:
\[ BD = DC = \frac{BC}{2} = \frac{48}{2} = 24 \text{ cm} \]

### Step 6: Use the Pythagorean theorem to find AB
In triangle ABD, we can apply the Pythagorean theorem:
\[ AB^2 = AD^2 + BD^2 \]
Substituting the known values:
\[ AB^2 = 7^2 + 24^2 \]
Calculating the squares:
\[ AB^2 = 49 + 576 = 625 \]

### Step 7: Take the square root to find AB
Now, take the square root:
\[ AB = \sqrt{625} = 25 \text{ cm} \]

### Conclusion
The length of one of the equal sides AB (or AC) is **25 cm**.

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