Chapter 3.5, Problem 57SR

To determine

Find x and y such that $\overline{BE}\text{ and }\overline{AD}$ are perpendicular.

Answer to Problem 57SR

x = 10

  $y=\frac{25}{3}$

Explanation of Solution

Given :

  

Calculation :

For $\overline{BE}\text{ and }\overline{AD}$ to be perpendicular , the angle between them should be right angle.

So, $\angle BFD=90°$ and $\angle AFE=90°$

Hence ,

  $\begin{array}{l}\angle BFD=90°\\ \Rightarrow 6x+3x=90\\ \Rightarrow 9x=90\\ \Rightarrow x=\frac{90}{9}\mathrm{...........}[\text{divide each side by 9]}\\ \Rightarrow x=10\end{array}$

and

  $\begin{array}{l}\angle AFE=90°\\ \Rightarrow 12y-10=90\\ \Rightarrow 12y=90+\mathrm{10......}[\text{add 10 each side]}\\ \Rightarrow 12y=100\\ \Rightarrow y=\frac{100}{12}=\frac{25}{3}\end{array}$

So,

x = 10

  $y=\frac{25}{3}$