Question

vishal is building a gazebo and wants to brace each corner by placing a 16 inch wooden bracket diagonally as shown. How far below the corner should he fasten the bracket if he wants the distances from each corner to be equal?

Answer 1

`8\sqrt[]{2}`

Step-by-step explanation:

The triangle formed by the wooden bracket and the sides is shown below

The distance labeled x is the distance from the corner.

Note that the vertical side and the horizontal sides are both X away from the corner as demanded.

Now, the Pythagorean theorem says that

`x^2+x^2=16^2`

which simplifies to give

`2x^2=16^2`

Dividing both sides by 2 gives

`(2x^2)/(2)=(16^2)/(2)`
`x^2=(16^2)/(2)`

Finally, taking the square root of both sides gives

`\sqrt[]{x^2}=\sqrt[]{(16^2)/(2)}`
`x=\frac{16}{\sqrt[]{2}}`
`x=8\sqrt[]{2}`

which is our answer!