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

This math topic focuses on applying the Pythagorean Theorem to find the lengths of sides in right triangles, expressed as square root values. Each problem presents a triangle with labeled sides, and the goal is to determine the length of one or more missing sides using the formula \(a^2 + b^2 = c^2\). These exercises help in understanding and manipulating radical expressions as part of a foundational approach to learning Pythagorean relationships in geometrical contexts.

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

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Pythagorean Theorem - Length of Side - 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 b=square root of 175
b A LaTex expression showing b=square root of 225
c A LaTex expression showing b=square root of 275
d A LaTex expression showing b=square root of 75
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 b=square root of 338
b A LaTex expression showing b=square root of 388
c A LaTex expression showing b=square root of 96
d A LaTex expression showing b=square root of 217
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 b=square root of 218
b A LaTex expression showing b=square root of 56
c A LaTex expression showing b=square root of 187
d A LaTex expression showing b=square root of 268
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 b=square root of 206
b A LaTex expression showing b=square root of 327
c A LaTex expression showing b=square root of 85
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 b=square root of 359
b A LaTex expression showing b=square root of 238
c A LaTex expression showing b=square root of 367
d A LaTex expression showing b=square root of 117
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 b=square root of 20
b A LaTex expression showing b=square root of 56
c A LaTex expression showing b=square root of 92
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 b=square root of 72
b A LaTex expression showing b=square root of 234
c A LaTex expression showing b=square root of 153
d A LaTex expression showing b=square root of 252
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 b=square root of 153
b A LaTex expression showing b=square root of 217
c A LaTex expression showing b=square root of 39
d A LaTex expression showing b=square root of 167