Math Problem Statement

Find the length of PZ (denoted as x) in the right-angled triangle PZT where ZT = 4 and PT = 5.

Solution

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

  • PZPZ is the perpendicular (height).
  • ZTZT is the base.
  • PTPT is the hypotenuse.
  • ZT=4ZT = 4
  • PT=5PT = 5
  • PZ=xPZ = x (unknown, needs to be determined).

Using the Pythagorean theorem: a2+b2=c2a^2 + b^2 = c^2 where:

  • a=PZ=xa = PZ = x,
  • b=ZT=4b = ZT = 4,
  • c=PT=5c = PT = 5,

we substitute the values:

x2+42=52x^2 + 4^2 = 5^2

x2+16=25x^2 + 16 = 25

x2=9x^2 = 9

x=9=3x = \sqrt{9} = 3

Thus, PZ=x=3PZ = x = 3.

Would you like a further explanation or a breakdown of the Pythagorean theorem?

Related Questions:

  1. How do you determine if a triangle is a right triangle using side lengths?
  2. What is the significance of the Pythagorean theorem in geometry?
  3. How can the Pythagorean theorem be applied in real-life situations?
  4. What happens if a triangle has sides that do not satisfy the Pythagorean theorem?
  5. How do you calculate the area and perimeter of a right triangle?

Tip:

Always check if a triangle satisfies the Pythagorean theorem before assuming it is a right triangle!

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Math Problem Analysis

Mathematical Concepts

Geometry
Right-angled triangles
Pythagorean theorem

Formulas

a^2 + b^2 = c^2

Theorems

Pythagorean theorem

Suitable Grade Level

Grades 6-8