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Pythagorean Theorem - Variable-Named Sides to Square Root Equation (Level 1)

This math topic focuses on applying the Pythagorean Theorem to find the length of a side in a right triangle. Each problem presents a different triangle with variable-named sides, requiring the learner to express the missing side length as a square root equation. The answers involve solving for the side using either addition or subtraction of the squares of the other two sides under a square root, illustrating the principles of the Pythagorean Theorem. This set of problems is part of an introductory unit on Pythagoras, emphasizing fundamental algebraic manipulations in geometry contexts.

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

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Variable-Named Sides to Square Root Equation

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Find the length of the side x as an equation based on the Pythagorean theorem

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Pythagorean Theorem - Variable-Named Sides to Square Root Equation Worksheet

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Math worksheet on 'Pythagorean Theorem - Variable-Named Sides to Square Root Equation (Level 1)'. Part of a broader unit on 'Pythagoras - Intro' Learn online: app.mobius.academy/math/units/pythagoras_intro/
1
An svg image showing a math problem
Find the length of the side z as an equation based on the Pythagorean theorem
a A LaTex expression showing z = square root of r to the power of 2 - m to the power of 2
b A LaTex expression showing z = square root of r to the power of 2 + m to the power of 2
2
An svg image showing a math problem
Find the length of the side d as an equation based on the Pythagorean theorem
a A LaTex expression showing d = square root of m to the power of 2 + r to the power of 2
b A LaTex expression showing d = square root of m to the power of 2 - r to the power of 2
3
An svg image showing a math problem
Find the length of the side p as an equation based on the Pythagorean theorem
a A LaTex expression showing p = square root of d to the power of 2 - m to the power of 2
b A LaTex expression showing p = square root of d to the power of 2 + m to the power of 2
4
An svg image showing a math problem
Find the length of the side d as an equation based on the Pythagorean theorem
a A LaTex expression showing d = square root of r to the power of 2 + p to the power of 2
b A LaTex expression showing d = square root of r to the power of 2 - p to the power of 2
5
An svg image showing a math problem
Find the length of the side y as an equation based on the Pythagorean theorem
a A LaTex expression showing y = square root of x to the power of 2 - m to the power of 2
b A LaTex expression showing y = square root of x to the power of 2 + m to the power of 2
6
An svg image showing a math problem
Find the length of the side p as an equation based on the Pythagorean theorem
a A LaTex expression showing p = square root of y to the power of 2 + r to the power of 2
b A LaTex expression showing p = square root of y to the power of 2 - r to the power of 2
7
An svg image showing a math problem
Find the length of the side p as an equation based on the Pythagorean theorem
a A LaTex expression showing p = square root of d to the power of 2 - m to the power of 2
b A LaTex expression showing p = square root of d to the power of 2 + m to the power of 2