Math Problem Statement

Given a right triangle with the longer two sides of 12 and 3√13, find the remaining shortest side.

Solution

The remaining shortest side of the right triangle is 33-3\sqrt{3}. However, since the length of a side cannot be negative, the correct positive value is 333\sqrt{3}, which corresponds to option c.

Do you need more details or have any questions?

Here are five related questions to expand the topic:

  1. How do you apply the Pythagorean theorem to solve for the sides of a right triangle?
  2. What happens if both legs of the right triangle are equal?
  3. Can the lengths of a triangle's sides ever be negative?
  4. How does the Pythagorean theorem change in non-Euclidean geometry?
  5. What other methods can you use to find missing sides in triangles besides the Pythagorean theorem?

Tip: Always check if the sides of the triangle you're calculating make sense in the context of the problem—lengths must be positive.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangle
Square Roots

Formulas

Pythagorean theorem: a² + b² = c²

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10