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

Question

not very sure how to solve this 

Answer 1

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

 

 

 

Answer 2

9/√(2) = x/1; remember Special Triangle 45°-45°-90°?

 

x = (9/√(2))/2 ≈ 6.36396103067893

Answer 3

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.