The base of a triangle is four times its height and its area is `50 m^(2)`. The length of its base is

Options

A. 10 m
B. 15 m
C. 20 m
D. 25 m

Answer

To find the length of the base of the triangle given that its base is four times its height and its area is 50 m², we can follow these steps:

### Step-by-Step Solution:

1. **Let the height of the triangle be \( x \)**:
\[ \text{Height} = x \text{ meters} \]

2. **Express the base in terms of height**:
Since the base is four times the height:
\[ \text{Base} = 4x \text{ meters} \]

3. **Use the formula for the area of a triangle**:
The area \( A \) of a triangle is given by:
\[ A = \frac{1}{2} \times \text{Base} \times \text{Height} \]
Substituting the known values:
\[ 50 = \frac{1}{2} \times (4x) \times x \]

4. **Simplify the equation**:
\[ 50 = \frac{1}{2} \times 4x^2 \]
\[ 50 = 2x^2 \]

5. **Solve for \( x^2 \)**:
Divide both sides by 2:
\[ x^2 = \frac{50}{2} = 25 \]

6. **Take the square root of both sides**:
\[ x = \sqrt{25} = 5 \text{ meters} \]

7. **Find the base using the value of \( x \)**:
Substitute \( x \) back into the expression for the base:
\[ \text{Base} = 4x = 4 \times 5 = 20 \text{ meters} \]

### Conclusion:
The length of the base of the triangle is **20 meters**.

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