Find the area of a right triangle whose hypotenuse measures 17 cm and one of the other two sides 8 cm .

Options

A. `=65 cm^(2)`.
B. `=50 cm^(2)`.
C. `=60 cm^(2)`.
D. `=70 cm^(2)`.

Answer

To find the area of a right triangle with a hypotenuse of 17 cm and one side measuring 8 cm, we can follow these steps:

### Step 1: Draw the Triangle
First, draw a right triangle and label the vertices as \( A \), \( B \), and \( C \). Let \( AC \) be the hypotenuse, \( BC \) be one of the other sides (8 cm), and \( AB \) be the other side we need to find.

### Step 2: Apply the Pythagorean Theorem
According to the Pythagorean theorem, for a right triangle:
\[ AC^2 = AB^2 + BC^2 \]
Here, \( AC = 17 \) cm and \( BC = 8 \) cm. We can rearrange the formula to find \( AB \):
\[ AB^2 = AC^2 - BC^2 \]

### Step 3: Substitute the Values
Now, substitute the values into the equation:
\[ AB^2 = 17^2 - 8^2 \]
Calculating the squares:
\[ AB^2 = 289 - 64 \]

### Step 4: Perform the Subtraction
Now, subtract the values:
\[ AB^2 = 225 \]

### Step 5: Take the Square Root
To find \( AB \), take the square root of both sides:
\[ AB = \sqrt{225} = 15 \text{ cm} \]

### Step 6: Calculate the Area of the Triangle
The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In our triangle, we can take \( AB \) as the height and \( BC \) as the base:
\[ A = \frac{1}{2} \times AB \times BC = \frac{1}{2} \times 15 \times 8 \]

### Step 7: Simplify the Area Calculation
Now, calculate the area:
\[ A = \frac{1}{2} \times 15 \times 8 = \frac{120}{2} = 60 \text{ cm}^2 \]

### Final Answer
Thus, the area of the right triangle is \( 60 \text{ cm}^2 \).

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