Which of the following steps is incorrect while constructing a `DeltaXYZ`, given that `XY=8cm`, `YZ=9cm` and `XZ=10cm` ?
Step 1 : Draw a line segment YZ of length 9 cm.
Step 2 : With Y as centre, draw an arc of radius 8cm.
Step 3 : With Z as centre, draw an arc of radius 9cm.
Step 4 : Mark the point of intersection of arcs as X. Join XY and XZ.

Options

A. Only Step 1
B. Only Step 3
C. Both Step 2 and Step 3
D. Both Step 3 and Step 4

Answer

To determine which step is incorrect while constructing triangle \( \Delta XYZ \) with sides \( XY = 8 \, \text{cm} \), \( YZ = 9 \, \text{cm} \), and \( XZ = 10 \, \text{cm} \), we will analyze each step one by one.

### Step-by-Step Solution:

**Step 1:** Draw a line segment \( YZ \) of length \( 9 \, \text{cm} \).
- This step is correct. We need \( YZ \) to be \( 9 \, \text{cm} \) as per the given dimensions.

**Step 2:** With \( Y \) as the center, draw an arc of radius \( 8 \, \text{cm} \).
- This step is also correct. We are constructing side \( XY \) which is \( 8 \, \text{cm} \) long from point \( Y \).

**Step 3:** With \( Z \) as the center, draw an arc of radius \( 9 \, \text{cm} \).
- This step is incorrect. We should be drawing an arc with a radius of \( 10 \, \text{cm} \) from point \( Z \) because \( XZ \) is \( 10 \, \text{cm} \) long, not \( 9 \, \text{cm} \).

**Step 4:** Mark the point of intersection of arcs as \( X \). Join \( XY \) and \( XZ \).
- This step is correct. After marking point \( X \), we can join \( XY \) and \( XZ \) to complete the triangle.

### Conclusion:
The incorrect step in the construction is **Step 3**, where it incorrectly states to draw an arc of radius \( 9 \, \text{cm} \) from point \( Z \) instead of the correct radius of \( 10 \, \text{cm} \).