Answer:
[tex]x = 13[/tex]
Step-by-step explanation:
Given
See attachment
Required
Find x
From the attachment, we have:
[tex]BC = x + 4[/tex]
[tex]BD = 2x - 7[/tex]
[tex]GE = 51[/tex]
[tex]GF = 57[/tex]
Because both triangles are similar, we use the following equivalent ratios:
[tex]BC : BD = GE : GF[/tex]
Substitute values for each parameter
[tex]x + 4 : 2x- 7 = 51 : 57[/tex]
Convert to fractions
[tex]\frac{x + 4}{2x- 7} = \frac{51 }{ 57}[/tex]
Simplify the right-hand side
[tex]\frac{x + 4}{2x- 7} = \frac{17}{19}[/tex]
Cross Multiply
[tex]19(x + 4) = 17(2x - 7)[/tex]
[tex]19x + 76 = 34x - 119[/tex]
Collect Like Terms
[tex]19x - 34x = -76 - 119[/tex]
[tex]-15x = -195[/tex]
Solve for x
[tex]x = \frac{-195}{-15}[/tex]
[tex]x = 13[/tex]
