Length of Side - Labelled Sides (Equation) (Level 2)

This math topic focuses on applying the Pythagorean theorem to find the length of a missing side in right triangles. Problems require identifying the correct equation representation using the theorem \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the legs of the triangle and \(c\) is the hypotenuse. Each problem provides multiple answer choices involving mathematical expressions like sums and differences of squares, challenging students to perform accurate calculations and comprehend algebraic representations.

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

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

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Math worksheet on 'Pythagorean Theorem - Length of Side - Labelled Sides (Equation) (Level 2)'. 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 an equation based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=10 to the power of 2 + 13 to the power of 2
b A LaTex expression showing b=square root of 10 to the power of 2 - 13 to the power of 2
c A LaTex expression showing b=10 to the power of 2 - 13 to the power of 2
d A LaTex expression showing b=square root of 13 to the power of 2 + 10 to the power of 2
e A LaTex expression showing b=square root of 13 to the power of 2 - 10 to the power of 2
2
Find the length of the missing side as an equation based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=square root of 12 to the power of 2 + 5 to the power of 2
b A LaTex expression showing b=square root of 12 to the power of 2 - 5 to the power of 2
c A LaTex expression showing b=5 to the power of 2 - 12 to the power of 2
d A LaTex expression showing b=5 to the power of 2 + 12 to the power of 2
3
Find the length of the missing side as an equation based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=square root of 14 to the power of 2 - 8 to the power of 2
b A LaTex expression showing b=square root of 8 to the power of 2 - 14 to the power of 2
c A LaTex expression showing b=square root of 8 to the power of 3 + 14 to the power of 3
d A LaTex expression showing b=8 to the power of 2 - 14 to the power of 2
e A LaTex expression showing b=square root of 14 to the power of 2 + 8 to the power of 2
4
Find the length of the missing side as an equation based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=6 to the power of 2 + 12 to the power of 2
b A LaTex expression showing b=square root of 12 to the power of 2 - 6 to the power of 2
c A LaTex expression showing b=6 to the power of 2 - 12 to the power of 2
d A LaTex expression showing b=square root of 12 to the power of 2 + 6 to the power of 2
5
Find the length of the missing side as an equation based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=square root of 9 to the power of 3 + 11 to the power of 3
b A LaTex expression showing b=9 to the power of 2 - 11 to the power of 2
c A LaTex expression showing b=square root of 11 to the power of 2 - 9 to the power of 2
d A LaTex expression showing b=9 to the power of 2 + 11 to the power of 2
6
Find the length of the missing side as an equation based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=8 to the power of 2 + 14 to the power of 2
b A LaTex expression showing b=square root of 8 to the power of 2 - 14 to the power of 2
c A LaTex expression showing b=8 to the power of 2 - 14 to the power of 2
d A LaTex expression showing b=square root of 14 to the power of 2 - 8 to the power of 2
7
Find the length of the missing side as an equation based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing b=square root of 13 to the power of 2 - 7 to the power of 2
b A LaTex expression showing b=7 to the power of 2 + 13 to the power of 2
c A LaTex expression showing b=square root of 7 to the power of 2 - 13 to the power of 2
d A LaTex expression showing b=7 to the power of 2 - 13 to the power of 2