Question

Use the figure to find the values of x, y, and Z that makes triangle DEF similar to triangle GHF.

Answer 1

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;

`m\angle E=m\angle G`

Given the following parameters;

mm

Equating the angles to determine the value of "x"

`\begin{gathered} 2(x-4)=16 \\ 2x-8=16 \\ 2x=16+8 \\ 2x=24 \\ x=12 \end{gathered}`

In order to determine the values of y and z, we will use the ratio of their similar sides to have;

`(FE)/(ED)=(FG)/(GH)`

Substitute the given sides

`\begin{gathered} (x-5)/(25)=(14)/(6z+8) \\ (12-5)/(25)=(14)/(6z+8) \\ (7)/(25)=(14)/(6z+8) \\ \end{gathered}`

Cross multiply

`\begin{gathered} 7(6z+8)=25(14) \\ 42z+56=350 \\ 42z=350-56 \\ 42z=294 \\ z=(294)/(42) \\ z=7 \end{gathered}`

Similarly to get the value of "y", we will use the ratios;

`\begin{gathered} (FH)/(FG)=(FD)/(FE) \\ (3y)/(14)=(24)/(x-5) \\ (3y)/(14)=(24)/(12-5) \\ (3y)/(14)=(24)/(7) \\ 21y=336 \\ y=(336)/(21) \\ y=16 \end{gathered}`

Therefore the values of x, y, and z that make triangle DEF similar to triangle GHF are 12, 16, and 7 respectively.