Answer:
x = 12
y = 16
z = 7
Explanations:
From the given question, we are told that triangle DEF is similar to triangle GHF. This invariably means;
[tex]m\angle E=m\angle G[/tex]
Given the following parameters;
mm
Equating the angles to determine the value of "x"
[tex]\begin{gathered} 2(x-4)=16 \\ 2x-8=16 \\ 2x=16+8 \\ 2x=24 \\ x=12 \end{gathered}[/tex]
In order to determine the values of y and z, we will use the ratio of their similar sides to have;
[tex]\frac{FE}{ED}=\frac{FG}{GH}[/tex]
Substitute the given sides
[tex]\begin{gathered} \frac{x-5}{25}=\frac{14}{6z+8} \\ \frac{12-5}{25}=\frac{14}{6z+8} \\ \frac{7}{25}=\frac{14}{6z+8} \\ \end{gathered}[/tex]
Cross multiply
[tex]\begin{gathered} 7(6z+8)=25(14) \\ 42z+56=350 \\ 42z=350-56 \\ 42z=294 \\ z=\frac{294}{42} \\ z=7 \end{gathered}[/tex]
Similarly to get the value of "y", we will use the ratios;
[tex]\begin{gathered} \frac{FH}{FG}=\frac{FD}{FE} \\ \frac{3y}{14}=\frac{24}{x-5} \\ \frac{3y}{14}=\frac{24}{12-5} \\ \frac{3y}{14}=\frac{24}{7} \\ 21y=336 \\ y=\frac{336}{21} \\ y=16 \end{gathered}[/tex]
Therefore the values of x, y, and z that make triangle DEF similar to triangle GHF are 12, 16, and 7 respectively.
