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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 
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3 Answers

Hi Marisa;
Because this is a square, a=b...
Let's divide both sides by 2...
square-root both sides...
9/√(2) = x/1; remember Special Triangle 45°-45°-90°?
x = (9/√(2))/2 ≈ 6.36396103067893
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.