The area of a right triangle is `40 cm^(2)`. If one of its legs measures 8 cm, find the length of the other leg.

Options

A. 6 cm
B. 8 cm
C. 10 cm
D. 16 cm

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the formula for the area of a triangle
The area \( A \) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, one leg of the triangle acts as the base, and the other leg acts as the height.

### Step 2: Assign the known values
From the problem, we know:
- The area \( A = 40 \, \text{cm}^2 \)
- One leg (base) \( b = 8 \, \text{cm} \)

### Step 3: Substitute the known values into the area formula
Using the area formula, we can substitute the known values:
\[ 40 = \frac{1}{2} \times 8 \times h \]

### Step 4: Simplify the equation
First, simplify the right side:
\[ 40 = 4 \times h \]

### Step 5: Solve for the height (the other leg)
Now, divide both sides by 4 to find \( h \):
\[ h = \frac{40}{4} = 10 \, \text{cm} \]

### Conclusion
The length of the other leg (height) is \( 10 \, \text{cm} \).

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