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If the diagonal of a square is 9 units long, how long is each side

not very sure how to solve this

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
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Hi Marisa;
a2+b2=c2
a2+b2=92
Because this is a square, a=b...
2a2=92
2a2=81
Let's divide both sides by 2...
(2a2)/2=81/2
a2=40.5
square-root both sides...
√a2=√40.5
a=6.36

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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9/√(2) = x/1; remember Special Triangle 45°-45°-90°?

x = (9/√(2))/2 ≈ 6.36396103067893
Bryce R. | UF Chemistry and Mathematics TutorUF Chemistry and Mathematics Tutor
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The diagonal cuts the square into two congruent triangles. Since it's a square, one of the corners will have a 90 degree angle, and the other two will have 45 degree angles since the triangle was cut out of a square. With the angle measurements known, you can use trigonometric functions in order to find the other sides. Ex: sin(45)=x/9 now you can solve x to find the missing side. Since it is a square, all other sides will have the same measurement.