Question

John is building a gazebo and wants to brace each corner by placing a 9-inch wooden bracket diagonally as shown. How far belo the corner should he fasten the bracket if he wants the distances from the corner to each end of the bracket to be equal?

Answer 1

6.4 inches

Step-by-step explanation:

The corner makes a triangle:

We would be applying pythagoras' theorem:

Hypotenuse² = opposite² + adjacent²

opposite = adjacent = x

hypotenuse = 9 in

9² = x² + x²

9² = 2x²

81 = 2x²

81/2 = x²

40.5 = x²

square root both sides:

x = √40.5

x = 6.36

To the nearest tenth, it will be 6.4 inches