The base of a right-angled triangle is 16 and hypotenuse is 20. What is its area?

Options

A. 96 `m^2`
B. 68 `m^2`
C. 58 `m^2`
D. 52 `m^2`

Answer

To find the area of a right-angled triangle with a base of 16 units and a hypotenuse of 20 units, we can follow these steps:

### Step 1: Identify the known values
We know the following:
- Base (b) = 16 units
- Hypotenuse (c) = 20 units

### Step 2: Use the Pythagorean theorem
In a right-angled triangle, the Pythagorean theorem states that:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is the height (or the other leg of the triangle),
- \( b \) is the base,
- \( c \) is the hypotenuse.

### Step 3: Substitute the known values into the equation
We can rearrange the equation to solve for \( a^2 \):
\[ a^2 + 16^2 = 20^2 \]
\[ a^2 + 256 = 400 \]

### Step 4: Solve for \( a^2 \)
Subtract 256 from both sides:
\[ a^2 = 400 - 256 \]
\[ a^2 = 144 \]

### Step 5: Find the height \( a \)
Now, take the square root of both sides to find \( a \):
\[ a = \sqrt{144} \]
\[ a = 12 \] units

### Step 6: Calculate the area of the triangle
The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Substituting the values we have:
\[ A = \frac{1}{2} \times 16 \times 12 \]

### Step 7: Perform the multiplication
\[ A = \frac{1}{2} \times 192 \]
\[ A = 96 \] square units

### Final Answer
The area of the triangle is 96 square units.

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