Math Problem Statement

Find the hypotenuse of the right-angled triangle PZT where PZ = 4 and PT = 3.

Solution

The given image shows a right-angled triangle PZT, where:

  • PZ = 4 (one leg)
  • PT = 3 (another leg)
  • ZT = x (hypotenuse)

To find x, we use the Pythagorean theorem:

x2=32+42x^2 = 3^2 + 4^2

x2=9+16x^2 = 9 + 16

x2=25x^2 = 25

x=25=5x = \sqrt{25} = 5

Answer:

x=5x = 5

Would you like a step-by-step explanation or have any questions?

Related Questions:

  1. What is the Pythagorean theorem, and when is it used?
  2. How do you determine if a given triangle is a right triangle?
  3. Can you use the Pythagorean theorem for non-right triangles?
  4. What are Pythagorean triplets, and how do they relate to this problem?
  5. How can you find missing side lengths using trigonometric ratios?

Tip: In a right triangle, the hypotenuse is always the longest side!

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Math Problem Analysis

Mathematical Concepts

Geometry
Right-Angled Triangles
Pythagorean Theorem

Formulas

x^2 = a^2 + b^2
x = √(a^2 + b^2)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 6-9