Question

William is building a gazebo and wants to brace each Corner replacing a 12 inch wooden bracket diagonally as shown how far below the corner should he fastened the bracket if he wants to distances from the corner to eat to the end of the bracket to be equal

Answer 1

Let the distance from the corner is x.

The length of diagonal -12 inch.

the fiure show a right angle triangle

Apply the pythagoras theorem to find the values of x

Pytahgoras theorem state as the square of the hypotenuse is equal to sum of the squre of perpendicular and the square of base of right angle triangle,

`\text{Hypotenuse}^2=Perpendicular^2+base^2`

In the given figure we have,

Hypotenuse=12

Base=x

Perpendicular=x

Substutute the value in the pythagoras theorem

`\begin{gathered} 12^2=x^2+x^2 \\ 144=2x^2 \\ x^2=72 \\ x=8.485 \\ x=8.5\text{inch} \end{gathered}`

The corner will be at a distance of 8.5 inch.