Problem preview
G-GMD.6 Warmup M2-040-A11-V01

Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.

Intersect a third-side interval with an extra constraint

Problem

Determine feasible third-side values under these constraints: fixed sides \(6\) and \(10\); third side \(x\) must be an integer.

Big Picture

What this problem is really about

The geometric interval should be established before the extra discrete condition is applied. We’ll derive strict lower and upper bounds from the difference and sum of the fixed sides, intersect that open interval with the integer requirement, and check both endpoints when listing the complete feasible set.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-GMD.6
Category
Geometry
Domain
Geometric Measurement and Dimension
Objective
Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.
Problem type
Intersect a third-side interval with an extra constraint