Length of Hypotenuse - Labelled Sides (Radical) (Level 1)

This math topic focuses on applying the Pythagorean Theorem to find the length of the hypotenuse or other sides of a right triangle, expressed as a radical (square root) value. The problems provide diagrams of triangles with sides labeled, where students are tasked with calculating unknown side lengths using the relationship \( a^2 + b^2 = c^2 \). This is foundational for understanding distances on a Cartesian grid, an introductory concept related to distance calculation in coordinate geometry. Each question offers a visual and the precise length expression required, enhancing visual learning and algebraic manipulation skills.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Pythagorean Theorem - Length of Hypotenuse - Labelled Sides (Radical) Worksheet

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Math worksheet on 'Pythagorean Theorem - Length of Hypotenuse - Labelled Sides (Radical) (Level 1)'. Part of a broader unit on 'Pythagoras - Intro' Learn online: app.mobius.academy/math/units/pythagoras_intro/
1
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing c=square root of 20
b A LaTex expression showing c=square root of -20
c A LaTex expression showing c=square root of 52
2
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing c=square root of 76
b A LaTex expression showing c=square root of 40
c A LaTex expression showing c=square root of 32
3
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing c=square root of 40
b A LaTex expression showing c=square root of 32
c A LaTex expression showing c=square root of 44
4
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing c=square root of 25
b A LaTex expression showing c=square root of 41
c A LaTex expression showing c=square root of 7
5
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing c=square root of 20
b A LaTex expression showing c=square root of 36
c A LaTex expression showing c=square root of 12
6
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing c=square root of 57
b A LaTex expression showing c=square root of 7
c A LaTex expression showing c=square root of 25
d A LaTex expression showing c=square root of 41
7
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing c=square root of 5
b A LaTex expression showing c=square root of 21
c A LaTex expression showing c=square root of 13