Question

18. A rectangular wooden gate with two diagonalboards across the front is shown below.x11 feetIP the length of one of the diagonals is 14 feet,find the closest value of x, the width of the gate.A 3 feetB. 17.8 feetC. 8,7 feetD. 75 Peer

Answer 1

From the question, we can make another sketch:

From this sketch, we can see that it is a right triangle problem that can be

solve using the Pythagoras theorem

`\begin{gathered} \text{hypotenuse}^2=adjacent^2+opposite^2 \\ \text{From the sketch above } \\ \text{hypotenuse side = 14ft} \\ \text{adjacent side =11ft} \\ \text{opposite side = x } \end{gathered}`
`\begin{gathered} \text{hypotenuse}^2=adjacent^2+opposite^2 \\ 14^2=11^2+x^2 \\ 14^2-11^2=x^2 \\ 196-121=x^2 \end{gathered}`
`\begin{gathered} 75=x^2 \\ \sqrt[]{75}=\sqrt[]{x^2} \\ 8.660ft\text{ =x} \\ \text{8}.7ft(to\text{ 1 decimal place)=x} \end{gathered}`

The correct option is C