BE and CF are two altitudes of a triangle ABC. If `AB = 6 cm, AC = 5 cm `and `CF = 4 cm`, then the length of BE is

Options

A. 4.8 cm
B. 7.5 cm
C. 3.33 cm
D. 5.5 cm

Answer

To find the length of BE in triangle ABC, we can follow these steps:

### Step 1: Calculate the area of triangle ABC using base AB and height CF.
The area \( A \) of triangle ABC can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, we take \( AB \) as the base and \( CF \) as the height. Given:
- \( AB = 6 \, \text{cm} \)
- \( CF = 4 \, \text{cm} \)

Substituting the values into the formula:
\[ A = \frac{1}{2} \times 6 \times 4 = \frac{24}{2} = 12 \, \text{cm}^2 \]

### Step 2: Set up the equation for the area using base AC and height BE.
Now, we will use \( AC \) as the base and \( BE \) as the height. The area can also be expressed as:
\[ A = \frac{1}{2} \times AC \times BE \]
Given:
- \( AC = 5 \, \text{cm} \)

Substituting the known area into the equation:
\[ 12 = \frac{1}{2} \times 5 \times BE \]

### Step 3: Solve for BE.
To isolate \( BE \), we first multiply both sides of the equation by 2:
\[ 24 = 5 \times BE \]
Now, divide both sides by 5:
\[ BE = \frac{24}{5} = 4.8 \, \text{cm} \]

### Conclusion:
The length of BE is \( 4.8 \, \text{cm} \).

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