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.

more
View

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

Mobius Math Academy logo
Pythagorean Theorem - Length of Hypotenuse - Labelled Sides (Radical)
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 52
b A LaTex expression showing c=square root of 20
c A LaTex expression showing c=square root of 68
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 13
b A LaTex expression showing c=square root of 21
c A LaTex expression showing c=square root of 5
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 5
b A LaTex expression showing c=square root of 13
c A LaTex expression showing c=square root of 22
d A LaTex expression showing c=square root of 31
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 21
b A LaTex expression showing c=square root of 33
c A LaTex expression showing c=square root of 29
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 41
b A LaTex expression showing c=square root of 9
c A LaTex expression showing c=square root of 73
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 48
b A LaTex expression showing c=square root of 32
c A LaTex expression showing c=square root of 0
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 27
b A LaTex expression showing c=square root of 54
c A LaTex expression showing c=square root of 45
d A LaTex expression showing c=square root of 63
8
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 107
b A LaTex expression showing c=square root of 156
c A LaTex expression showing c=square root of 58
d A LaTex expression showing c=square root of 40