Question

Alice is building a gazebo and wants to brace each corner by placing a 14 inch wooden bracket diagonally as shown. How far below each corner shouls she fasten the bracketbif she wants the dist3 from each end of the bracket to be equal?

Answer 1

The 14 inch wooden bracket form a right triangle with each end of the bracket:

The wooden bracket is the hypotenuse (h) of the right triangle. Use the pythagorean theorem to find the lenght of sides x (both sides have the same length)

`\begin{gathered} h^2=(leg_1)^2+(leg_2)^2 \\ \\ 14^2=x^2+x^2 \end{gathered}`

Use the equation above to find x:

`\begin{gathered} 196=2x^2 \\ (196)/(2)=x^2 \\ 98=x^2 \\ \sqrt[]{98}=x \\ \\ x\approx9.9 \end{gathered}`

Then, the bracket needs to be 9.9 inches to has the same distanced from each end.