`DeltaPQR` is right angled at Q and measure of side PQ =14 cm., then what is the length (in cm.,)of side QR ?

Options

A. A) 50
B. B) 20
C. C) 26
D. D) 48

Answer

To find the length of side QR in the right-angled triangle PQR, where PQ = 14 cm and the triangle is right-angled at Q, we can use the properties of Pythagorean triplets.

### Step-by-Step Solution:

1. **Identify the Right Triangle**:
We have triangle PQR, which is right-angled at Q. This means that the sides PQ and QR are the two legs of the triangle, and PR is the hypotenuse.

2. **Given Information**:
We know that PQ = 14 cm. We need to find the length of side QR.

3. **Use Pythagorean Triplets**:
Pythagorean triplets are sets of three positive integers a, b, and c, such that \(a^2 + b^2 = c^2\). For our case, we need to find a triplet that includes 14 as one of the legs.

4. **Finding the Triplet**:
A known triplet that includes 14 is (7, 24, 25). To use this, we can multiply the entire triplet by 2 to scale it up:
- \(7 \times 2 = 14\)
- \(24 \times 2 = 48\)
- \(25 \times 2 = 50\)

Thus, the triplet (14, 48, 50) corresponds to our triangle where:
- PQ = 14 cm
- QR = 48 cm (the side we want to find)
- PR = 50 cm (the hypotenuse)

5. **Conclusion**:
Therefore, the length of side QR is 48 cm.

### Final Answer:
The length of side QR is **48 cm**.