To solve for the length of ( YZ ) in the given right-angled triangle, we can again use the Pythagorean theorem.

Given:

• Side ( XY = 9 , \text{cm} )
• Side ( XZ = 16 , \text{cm} )
• Hypotenuse ( YZ ) (unknown)

Using the Pythagorean Theorem:

[ YZ^2 = XY^2 + XZ^2 ]

Substituting the Values:

[ YZ^2 = 9^2 + 16^2 ] [ YZ^2 = 81 + 256 ] [ YZ^2 = 337 ]

Solving for ( YZ ):

[ YZ = \sqrt{337} \approx 18.4 , \text{cm} ]

Final Answer:

The length of ( YZ ) is approximately 18.4 cm (rounded to 1 decimal place).

If you have any more questions or need further details, feel free to ask!

Here are some related questions you might find interesting:

1. What is the perimeter of the triangle with sides ( XY ), ( XZ ), and ( YZ )?
2. How would the area of the triangle change if ( XY ) were increased to 12 cm?
3. What would the length of ( YZ ) be if ( XZ ) was doubled?
4. How can you verify that ( YZ ) is the longest side in this triangle?
5. What is the ratio of ( XY ) to ( XZ )?

Tip: Always double-check your calculations, especially when dealing with square r