This math topic focuses on applying the Pythagorean theorem to calculate the side lengths of squares, given their diagonal lengths. Each problem presents a square with a known diagonal measurement and requires finding the sides' lengths in decimal form. The problems systematically increase the complexity by varying the diagonal measures, allowing practice of the theorem in progressively challenging scenarios. The topic is part of a larger unit dedicated to practicing Pythagorean theorem principles, specifically tailored for understanding the relationship between the square's diagonal and its side lengths.

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

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Pythagoras in Squares - Diagonal Hypotenuse to Side Decimal Worksheet

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Pythagoras in Squares - Diagonal Hypotenuse to Side Decimal
1
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Find the length of the square sides, given a diagonal of length 15
a
10.61
b
12.73
2
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Find the length of the square sides, given a diagonal of length 12
a
8.49
b
11.03
3
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Find the length of the square sides, given a diagonal of length 11
a
7.78
b
5.44
4
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Find the length of the square sides, given a diagonal of length 10
a
7.07
b
9.19
5
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Find the length of the square sides, given a diagonal of length 8
a
5.66
b
7.35
6
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Find the length of the square sides, given a diagonal of length 16
a
6.79
b
11.31
7
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Find the length of the square sides, given a diagonal of length 9
a
3.82
b
6.36
8
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Find the length of the square sides, given a diagonal of length 7
a
3.46
b
4.95