Math Problem Statement

The image shows four right triangles, each labeled with side lengths. The user likely needs to find the missing sides using the Pythagorean theorem.

Solution

The image shows four right triangles, each labeled with side lengths. These triangles appear to represent different cases of the Pythagorean theorem, where the relationship between the sides of a right triangle is given by:

a2+b2=c2a^2 + b^2 = c^2

Where aa and bb are the legs of the triangle, and cc is the hypotenuse.

Let’s break down each triangle based on the labels:

  1. First Triangle:

    • Leg 1 = 40
    • Leg 2 = Unknown
    • Hypotenuse = 41

    This forms a classic Pythagorean triple: 402+92=41240^2 + 9^2 = 41^2, meaning the other leg must be 9.

  2. Second Triangle:

    • Leg 1 = 80
    • Leg 2 = Unknown
    • Hypotenuse = 82

    This also forms a Pythagorean triple: 802+182=82280^2 + 18^2 = 82^2, so the missing leg is 18.

  3. Third Triangle:

    • Leg 1 = 24
    • Leg 2 = Unknown
    • Hypotenuse = 26

    Here, 242+102=26224^2 + 10^2 = 26^2, so the other leg is 10.

  4. Fourth Triangle:

    • Leg 1 = 12
    • Leg 2 = Unknown
    • Hypotenuse = 13

    This gives another classic Pythagorean triple: 122+52=13212^2 + 5^2 = 13^2, so the other leg is 5.

Would you like more detailed calculations or further explanations?


Here are some related questions to explore:

  1. How do you find the missing side of a right triangle using the Pythagorean theorem?
  2. What are Pythagorean triples, and why are they useful?
  3. How does the Pythagorean theorem apply in real-world scenarios?
  4. Can you derive the formula for the hypotenuse if both legs are given?
  5. What are some common mistakes when applying the Pythagorean theorem?

Tip: Always double-check if a triangle's side lengths form a known Pythagorean triple to simplify your work!

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Math Problem Analysis

Mathematical Concepts

Pythagorean Theorem
Right Triangles
Algebra

Formulas

a^2 + b^2 = c^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-10