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Pythagorean Theore

Either Missing Length (Equation) (Level 2)

This math topic focuses on applying the Pythagorean theorem to find the length of a missing side in right triangles. It provides multiple questions where students are required to set up and solve equations using the theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Each question presents a different triangle and asks for the calculation of a side’s length, reinforcing the theorem's concept through varied examples. The exercise may include checking the validity of provided expressions for these calculations.

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

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Either Missing Length (Equation)

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10

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

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Teaching Transcript

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Find the equation for the length of each side based on Pythagoras

First let's identify the hypotenuse. It's opposite the right angle, so 'P' squared equals 'D' squared plus 'Y' squared

Taking the square root of both sides, 'P' equals the root of 'D' squared plus 'Y' squared

For the other sides, we need to subtract from the square of the hypotenuse

And again, taking the root of both sides of the equation will give us the length of a leg side

Pythagorean Theorem - Either Missing Length (Equation) Worksheet

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Math worksheet on 'Pythagorean Theorem - Either Missing Length (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
An svg image showing a math problem
a A LaTex expression showing square root of 14 to the power of 2 - 11 to the power of 2
b A LaTex expression showing 11 to the power of 2 - 14 to the power of 2
c A LaTex expression showing 11 to the power of 2 + 14 to the power of 2
d A LaTex expression showing square root of 11 to the power of 2 - 14 to the power of 2
2
Find the length of the missing side as an equation based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing 8 to the power of 2 + 7 to the power of 2
b A LaTex expression showing square root of 8 to the power of 2 + 7 to the power of 2
c A LaTex expression showing 8 to the power of 2 - 7 to the power of 2
3
Find the length of the missing side as an equation based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing square root of 7 to the power of 2 - 11 to the power of 2
b A LaTex expression showing 7 to the power of 2 - 11 to the power of 2
c A LaTex expression showing square root of 7 to the power of 2 + 11 to the power of 2
4
Find the length of the missing side as an equation based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing 10 to the power of 2 + 6 to the power of 2
b A LaTex expression showing 10 to the power of 2 - 6 to the power of 2
c A LaTex expression showing square root of 6 to the power of 2 - 10 to the power of 2
d A LaTex expression showing square root of 10 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
An svg image showing a math problem
a A LaTex expression showing square root of 8 to the power of 2 + 10 to the power of 2
b A LaTex expression showing 8 to the power of 2 + 10 to the power of 2
c A LaTex expression showing 8 to the power of 2 - 10 to the power of 2
d A LaTex expression showing square root of 8 to the power of 2 - 10 to the power of 2
6
Find the length of the missing side as an equation based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing 10 to the power of 2 + 4 to the power of 2
b A LaTex expression showing square root of 10 to the power of 2 - 4 to the power of 2
c A LaTex expression showing square root of 10 to the power of 2 + 4 to the power of 2
d A LaTex expression showing 10 to the power of 2 - 4 to the power of 2
7
Find the length of the missing side as an equation based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing 9 to the power of 2 - 7 to the power of 2
b A LaTex expression showing square root of 9 to the power of 2 - 7 to the power of 2
c A LaTex expression showing 9 to the power of 2 + 7 to the power of 2
d A LaTex expression showing square root of 9 to the power of 2 + 7 to the power of 2