In `Delta ABC`, side BC = 10 cm and height AD = 4.4 cm If AC = 11 cm. then altitude BE equals -----

Options

A. 5 cm
B. 4 cm
C. 5.6 cm
D. 5.5 cm

Answer

To find the altitude BE in triangle ABC, we can use the area of the triangle calculated in two different ways. Let's break down the solution step by step.

### Step 1: Calculate the Area of Triangle ABC using Base BC and Height AD

The formula for the area of a triangle is given by:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

Here, we can take BC as the base and AD as the height.

Given:
- Base BC = 10 cm
- Height AD = 4.4 cm

Now, substituting the values into the area formula:
\[ \text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 4.4 \, \text{cm} \]
\[ \text{Area} = \frac{1}{2} \times 44 \, \text{cm}^2 = 22 \, \text{cm}^2 \]

### Step 2: Calculate the Area of Triangle ABC using Base AC and Height BE

Now, we will use AC as the base and BE as the height.

Given:
- Base AC = 11 cm
- Height BE = ?

Using the area formula again:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ 22 \, \text{cm}^2 = \frac{1}{2} \times 11 \, \text{cm} \times BE \]

### Step 3: Solve for BE

Now, we can solve for BE:
\[ 22 = \frac{1}{2} \times 11 \times BE \]
Multiplying both sides by 2 to eliminate the fraction:
\[ 44 = 11 \times BE \]

Now, divide both sides by 11:
\[ BE = \frac{44}{11} = 4 \, \text{cm} \]

### Conclusion

Thus, the altitude BE equals **4 cm**.

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