Free Printable WorksheetMathGeometryMath CurriculumG-SRT.B.4-5

GEO.107 Solve for missing lengths using geometric mean relationships Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.107 Solve for missing lengths using geometric mean relationships. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.107 Solve for missing lengths using geometric mean relationships - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.B.4-5. Skill statement in this prompt cell: Select the correct geometric-mean equation and compute the missing length. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.B.4-5; NY GEO G.G-SRT.B; MA G-SRT.B; FL MA.912.GR.1.2, 1.6. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Geometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related GEO.107 Solve for missing lengths using geometric mean relationships skill assessments:

Problem 1Difficulty: Mastery
A right triangle has altitude 18 to the hypotenuse. The hypotenuse segments are x and x + 15. If leg AC is adjacent to the shorter segment x, what is AC?
A18 units
B6 sqrt(13) units
C9 sqrt(5) units
D39 units
Solution & Explanation:The altitude gives x(x + 15) = 182 = 324. Solving x2 + 15x - 324 = 0 gives x = 12, so the hypotenuse is 12 + 27 = 39. The leg adjacent to x has AC2 = 39(12) = 468, so AC = 6 sqrt(13) units.
Problem 2Difficulty: Mastery
The altitude to the hypotenuse is 12 sqrt(5), and one hypotenuse segment is 20. What is the exact length of the leg adjacent to the other segment?
A12 sqrt(5) units
B12 sqrt(14) units
C24 sqrt(5) units
D56 units
Solution & Explanation:Square the altitude: (12 sqrt(5))2 = 720. Then 720 = 20q, so q = 36 and the whole hypotenuse is 56. The leg adjacent to q has length squared 56(36) = 2016, so the length is 12 sqrt(14) units.
Problem 3Difficulty: Mastery
A triangular brace forms a right triangle with hypotenuse 125 units and one leg 75 units. What are the other hypotenuse segment and the altitude to the hypotenuse?
Aother segment 45 units, altitude 60 units
Bother segment 80 units, altitude 60 units
Cother segment 80 units, altitude 75 units
Dother segment 100 units, altitude 45 units
Solution & Explanation:The segment adjacent to the 75-unit leg is p = 752/125 = 45. The other hypotenuse segment is 125 - 45 = 80. Then h2 = 45(80) = 3600, so h = 60 units.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this GEO.107 Solve for missing lengths using geometric mean relationships worksheet?

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QIs this GEO.107 Solve for missing lengths using geometric mean relationships worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Geometry Math students. It aligns with educational standard G-SRT.B.4-5 (Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.B.4-5. Skill statement in this prompt cell: Select the correct geometric-mean equation and compute the missing length. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.B.4-5; NY GEO G.G-SRT.B; MA G-SRT.B; FL MA.912.GR.1.2, 1.6. Use this prompt-provided wording as the supporting standard description for this workflow.).

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