Chapter 3, Problem 7RP

a

To determine

To calculate: Value of x and measure of $\angle G$

Answer to Problem 7RP

Value of x is $28$ and measure of $\angle G$ is $60°$ .

Explanation of Solution

Given information : $\Delta HGF$ is equilateral, $\angle F=(x+32)°$ and $\angle H=(2x+4)°$

Formula used : All angles of equilateral triangle are equal and are of $60°$ .

Calculation: As, angles of equilateral triangle are equal,

  $\begin{array}{l}\Rightarrow \angle F=\angle H\\ \Rightarrow (x+32)°=(2x+4)°\\ \Rightarrow 32-4=2x-x\\ \Rightarrow 28=x\\ \Rightarrow x=28\end{array}$

Now, as all angles of equilateral triangle are of $60°$ ,

  $\Rightarrow \angle G=60°$

b

To determine

To calculate: Perimeter of $\Delta HGF$

Answer to Problem 7RP

Perimeter of $\Delta HGF$ is $30$ units.

Explanation of Solution

Given information : $\Delta HGF$ is equilateral, perimeter is $6y+24$ and $HG=3y-7$

Formula used : Perimeter of equilateral triangle = $3$ (side)

Calculation: As, Perimeter of equilateral triangle is $3$ (side),

  $\begin{array}{l}\Rightarrow 6y+24=3(3y-7)\\ \Rightarrow 6y+24=9y-21\\ \Rightarrow 24-21=9y-6y\\ \Rightarrow 3=3y\\ \Rightarrow y=\frac{3}{3}\\ \Rightarrow y=1\end{array}$

Now, putting $y=1$ in $6y+24$ ,

  $\begin{array}{l}\Rightarrow 6(1)+24\\ \Rightarrow 6+24\\ \Rightarrow 30\end{array}$

  $\therefore$ Perimeter = $30$