`DeltaPQR ` is right angled at point Q. If `PQ = 8 cm `and `PR = (QR + 2) cm`. What is the value (in cm) of PR?

Options

A. 17
B. 15
C. 19
D. 18

Answer

To find the length of PR in triangle PQR, which is right-angled at Q, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Known Values:**
- We know that \( PQ = 8 \, \text{cm} \).
- Let \( QR = x \, \text{cm} \).
- Therefore, \( PR = QR + 2 = x + 2 \, \text{cm} \).

2. **Apply the Pythagorean Theorem:**
- According to the Pythagorean theorem, in a right-angled triangle:
\[ PR^2 = PQ^2 + QR^2 \]
- Substituting the known values:
\[ (x + 2)^2 = 8^2 + x^2 \]

3. **Expand the Equation:**
- Expanding the left side:
\[ x^2 + 4x + 4 = 64 + x^2 \]

4. **Simplify the Equation:**
- Subtract \( x^2 \) from both sides:
\[ 4x + 4 = 64 \]
- Now, subtract 4 from both sides:
\[ 4x = 60 \]

5. **Solve for x:**
- Divide both sides by 4:
\[ x = 15 \, \text{cm} \]

6. **Find PR:**
- Now, substitute \( x \) back to find \( PR \):
\[ PR = x + 2 = 15 + 2 = 17 \, \text{cm} \]

### Final Answer:
The length of \( PR \) is \( 17 \, \text{cm} \).

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