Length of Hypotenuse - Labelled Sides (Radical) (Level 2)

This math topic focuses on the application of the Pythagorean Theorem to find the lengths of missing sides in right triangles, specifically the hypotenuse. The problems require expressing the lengths as square root values and utilize labeled sides. These exercises help enhance skills in identifying the sides of triangles, applying the theorem formula \(a^2 + b^2 = c^2\), and simplifying radical expressions. The problems progress through a set of examples, providing solutions in radical form, thus deepening understanding of Pythagorean relationships and radical calculations.

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

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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 89
b A LaTex expression showing c=square root of 114
c A LaTex expression showing c=square root of 39
2
An svg image showing a math problem
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
a A LaTex expression showing c=square root of 0
b A LaTex expression showing c=square root of 242
3
An svg image showing a math problem
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
a A LaTex expression showing c=square root of 64
b A LaTex expression showing c=square root of 136
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 130
b A LaTex expression showing c=square root of 32
c A LaTex expression showing c=square root of -32
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 117
b A LaTex expression showing c=square root of 45
c A LaTex expression showing c=square root of 279
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 89
b A LaTex expression showing c=square root of 114
c A LaTex expression showing c=square root of 39
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 268
b A LaTex expression showing c=square root of 170
c A LaTex expression showing c=square root of 219
d A LaTex expression showing c=square root of 72
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 181
b A LaTex expression showing c=square root of 19
c A LaTex expression showing c=square root of 381