The area of a right angled triangle is 40 sq cm. If its base is equal to 28 cm, find its height.

Options

A. `3 6/7 cm`
B. `4 6/7 cm`
C. `2 6/7 cm`
D. `5 6/7 cm`

Answer

To find the height of the right-angled triangle given the area and the base, we can use the formula for the area of a triangle.

### Step-by-Step Solution:

1. **Understand the formula for the area of a triangle**:
The area \( A \) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]

2. **Substitute the known values into the formula**:
Here, the area \( A \) is given as 40 sq cm, and the base is given as 28 cm. We can substitute these values into the formula:
\[ 40 = \frac{1}{2} \times 28 \times \text{height} \]

3. **Simplify the equation**:
First, calculate \( \frac{1}{2} \times 28 \):
\[ \frac{1}{2} \times 28 = 14 \]
So, the equation now becomes:
\[ 40 = 14 \times \text{height} \]

4. **Solve for height**:
To find the height, divide both sides of the equation by 14:
\[ \text{height} = \frac{40}{14} \]

5. **Simplify the fraction**:
To simplify \( \frac{40}{14} \):
\[ \text{height} = \frac{20}{7} \text{ cm} \]

### Final Answer:
The height of the triangle is \( \frac{20}{7} \) cm or approximately 2.86 cm.