Math Problem Statement

If the sides a, b, and c of a triangle satisfy a^2 + b^2 = c^2, then the triangle is a right triangle with legs having lengths a and b and the ________ having length c.

Solution

The given question is based on the Pythagorean Theorem, which states that for a right triangle with legs of lengths aa and bb and hypotenuse cc, the relation a2+b2=c2a^2 + b^2 = c^2 holds true.

In the question, it is specified that if the sides aa, bb, and cc satisfy a2+b2=c2a^2 + b^2 = c^2, then cc must represent the hypotenuse. Thus, the correct answer is:

Hypotenuse

Would you like more details or have any further questions?

Here are some related questions:

  1. What is the Pythagorean Theorem?
  2. How can you identify the hypotenuse in a right triangle?
  3. Why is the Pythagorean Theorem applicable only to right triangles?
  4. What are some examples of Pythagorean triples?
  5. How do you find the length of a missing side in a right triangle using a2+b2=c2a^2 + b^2 = c^2?

Tip: Remember, in any right triangle, the hypotenuse is always opposite the right angle and is the longest side.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles

Formulas

Pythagorean Theorem: a^2 + b^2 = c^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-10