Answer:
[tex]EF = 18[/tex]
Step-by-step explanation:
Given
[tex]\triangle DE\ F[/tex] similar to [tex]\triangle JHI[/tex]
Required
Find [tex]EF[/tex]
[tex]\triangle DE\ F[/tex] similar to [tex]\triangle JHI[/tex] implies that:
The corresponding sides are:
[tex]DE \to JH[/tex]
[tex]DF \to JI[/tex]
[tex]EF \to HI[/tex]
[tex]FG \to IK[/tex]
First, solve for x using the following corresponding ratios
[tex]EF : HI = FG : IK[/tex]
This gives:
[tex]x + 8 : 3x - 2 = 9 : 14[/tex]
Express as fraction
[tex]\frac{x + 8 }{ 3x - 2} = \frac{9 }{ 14}[/tex]
Cross multiply
[tex]14(x + 8) = 9(3x - 2)[/tex]
Open brackets
[tex]14x + 112 = 27x - 18[/tex]
Collect like terms
[tex]27x - 14x = 112 + 18[/tex]
[tex]13x = 130[/tex]
Solve for x
[tex]x = 10[/tex]
In the diagram, we have:
[tex]EF = x +8[/tex]
[tex]EF = 10 +8[/tex]
[tex]EF = 18[/tex]
