Free Printable WorksheetMathGrade 8Math Curriculum8.G.B.7

8.151 Pythagorean Theorem Word Problems in Two and Three Dimensions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.151 Pythagorean Theorem Word Problems in Two and Three Dimensions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.151 Pythagorean Theorem Word Problems in Two and Three Dimensions - Which setup and solution correctly use the Pythagorean theorem to solve the word problem? (CCSS 8.G.B.7; CA 8.G.B.7; MA 8.G.B.7)

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

Grade 8

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 8.151 Pythagorean Theorem Word Problems in Two and Three Dimensions skill assessments:

Problem 1Difficulty: Hard
A display stand is 4 ft long and 17 ft wide. Its space diagonal is 33 ft. Which choice correctly finds the stand's height?
AUse x = 33 - 4 - 17, so the height is 12 ft
BUse x2 = 332 + 42 + 172, so the height is 37.3 ft
CUse x2 = 42 + 172, so the height is 17.5 ft
DUse x2 = 332 - 42 - 172, so the height is 28 ft
Solution & Explanation:Use d2 = l2 + w2 + h2 and solve for the unknown: x = sqrt(332 - 42 - 172) = sqrt(784) = 28, so the height is 28 ft.
Problem 2Difficulty: Hard
A storage crate measures 6 cm by 21 cm by 22 cm. Which student correctly finds the crate's space diagonal?
AEvan is correct because d2 = (6+21)2 + 222
BRina is correct because the longest distance is just the largest edge, 22 cm
CJamal is correct because d2 = 62 + 212 + 222, so d = 31 cm
DSofia is correct because d = 49 cm
Solution & Explanation:Apply the Pythagorean theorem in 3D: d = sqrt(62 + 212 + 222) = sqrt(961) = 31, so the space diagonal is 31 cm.
Problem 3Difficulty: Hard
A tool chest measures 4 ft by 20 ft by 22 ft. A metal bar is 31 ft long. Which statement is correct?
AYes. The largest edge is 22 ft, which is enough.
BYes. Add the three edges to get 46 ft, so that guarantees it will fit.
CYes. A face diagonal is always longer than the space diagonal.
DNo. The space diagonal is only 30 ft, so an object that is 31 ft is too long.
Solution & Explanation:Apply the Pythagorean theorem in 3D: d = sqrt(42 + 202 + 222) = sqrt(900) = 30, so the space diagonal is 30 ft.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.G.B.7 (Primary standard selected for prompt fields: CCSS 8.G.B.7. Skill statement: Which setup and solution correctly use the Pythagorean theorem to solve the word problem? Associated standards listed with this skill: CCSS 8.G.B.7; CA 8.G.B.7; MA 8.G.B.7. Use this embedded wording as the best available supporting standard description for this workflow.).

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