The length of the two sides forming the right angle of a right-angled triangle are 6 cm and 8 cm. The length of its circumradius is :

Options

A. A)5 cm
B. B)7 cm
C. C)6 cm
D. D)10 cm

Answer

To find the circumradius of a right-angled triangle with the lengths of the two sides forming the right angle given as 6 cm and 8 cm, we can follow these steps:

### Step 1: Identify the sides of the triangle
Let the two sides forming the right angle be:
- Side AB = 6 cm
- Side BC = 8 cm

### Step 2: Use the Pythagorean theorem to find the hypotenuse
The hypotenuse (AC) can be calculated using the Pythagorean theorem, which states:
\[ AC^2 = AB^2 + BC^2 \]

Substituting the values:
\[ AC^2 = 6^2 + 8^2 \]
\[ AC^2 = 36 + 64 \]
\[ AC^2 = 100 \]

Now, take the square root to find AC:
\[ AC = \sqrt{100} = 10 \, \text{cm} \]

### Step 3: Calculate the circumradius
In a right-angled triangle, the circumradius (R) is given by the formula:
\[ R = \frac{AC}{2} \]

Substituting the value of AC:
\[ R = \frac{10}{2} = 5 \, \text{cm} \]

### Conclusion
The length of the circumradius of the triangle is **5 cm**.

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