XYZ is a right angled triangle and `/_Y = 90^@`. If `XY = 2.5 `cm and `YZ = 6 `cm then the circumradius of `DeltaXYZ ` is :

Options

A. 6.5 cm
B. 3.25 cm
C. 3 cm
D. 2.5 cm

Answer

To find the circumradius of triangle XYZ, we will follow these steps:

### Step 1: Identify the sides of the triangle
In triangle XYZ, we know:
- \( XY = 2.5 \, \text{cm} \)
- \( YZ = 6 \, \text{cm} \)
- \( \angle Y = 90^\circ \)

### Step 2: Use the Pythagorean theorem to find the hypotenuse
The hypotenuse \( XZ \) can be calculated using the Pythagorean theorem, which states:
\[ XZ^2 = XY^2 + YZ^2 \]
Substituting the values:
\[ XZ^2 = (2.5)^2 + (6)^2 \]
Calculating the squares:
\[ XZ^2 = 6.25 + 36 \]
\[ XZ^2 = 42.25 \]

### Step 3: Calculate the length of the hypotenuse
Now, take the square root to find \( XZ \):
\[ XZ = \sqrt{42.25} = 6.5 \, \text{cm} \]

### Step 4: Find the circumradius
The circumradius \( R \) of a right triangle is given by the formula:
\[ R = \frac{XZ}{2} \]
Substituting the value of \( XZ \):
\[ R = \frac{6.5}{2} = 3.25 \, \text{cm} \]

### Final Answer
The circumradius of triangle XYZ is \( 3.25 \, \text{cm} \).

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