The base and perpendicular of a right angled triangle are 12 cm and 5 cm respectively. Find the circum-radius (in cm.) of the triangle.

Options

A. `5`
B. `6`
C. `6.5`
D. `7`

Answer

To find the circum-radius of a right-angled triangle with a base of 12 cm and a perpendicular height of 5 cm, we can follow these steps:

### Step 1: Identify the sides of the triangle
We have a right-angled triangle with:
- Base (b) = 12 cm
- Perpendicular (h) = 5 cm

### Step 2: Calculate the hypotenuse
Using the Pythagorean theorem, we can find the hypotenuse (c) of the triangle. The theorem states that in a right-angled triangle:

\[ c^2 = b^2 + h^2 \]

Substituting the values:

\[ c^2 = 12^2 + 5^2 \]
\[ c^2 = 144 + 25 \]
\[ c^2 = 169 \]

Now, take the square root to find the hypotenuse:

\[ c = \sqrt{169} = 13 \text{ cm} \]

### Step 3: Calculate the circum-radius
For a right-angled triangle, the circum-radius (R) can be calculated using the formula:

\[ R = \frac{c}{2} \]

Substituting the value of the hypotenuse:

\[ R = \frac{13}{2} = 6.5 \text{ cm} \]

### Final Answer
The circum-radius of the triangle is **6.5 cm**.

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