Math Problem Statement

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

Solution

It seems like the response got cut off towards the end. Let me complete it and provide the missing part:

Tip: Always double-check your calculations, especially when dealing with square roots and decimals, to avoid rounding errors.

Feel free to ask if you have any questions or would like to explore any of the related questions listed above!

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Math Problem Analysis

Mathematical Concepts

Geometry
Pythagorean Theorem

Formulas

Pythagorean theorem: YZ^2 = XY^2 + XZ^2

Theorems

Pythagorean theorem

Suitable Grade Level

Grades 7-9