Base of a right angled triangle is

Options

A. `sqrt(("Hypotenous")^(2)+("Perpendicular")^(2))`
B. `sqrt(("Hypotenous")^(2)-("Perpendicular")^(2))`
C. `sqrt(("Perpendicular")^(2)-("Hypotenous")^(2))`
D. None of These

Answer

To find the base of a right-angled triangle when given the hypotenuse and the perpendicular (height), we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Understand the components of the triangle
In a right-angled triangle, we have:
- Hypotenuse (the longest side opposite the right angle)
- Perpendicular (the side opposite the angle we are considering)
- Base (the side adjacent to the angle we are considering)

### Step 2: Write down the Pythagorean theorem
The Pythagorean theorem states that:
\[ \text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2 \]

### Step 3: Rearrange the formula to find the base
To find the base, we can rearrange the formula:
\[ \text{Base}^2 = \text{Hypotenuse}^2 - \text{Perpendicular}^2 \]

### Step 4: Take the square root
Now, to find the base, we take the square root of both sides:
\[ \text{Base} = \sqrt{\text{Hypotenuse}^2 - \text{Perpendicular}^2} \]

### Step 5: Conclusion
Thus, the base of the right-angled triangle can be calculated using the formula:
\[ \text{Base} = \sqrt{\text{Hypotenuse}^2 - \text{Perpendicular}^2} \]