Answer:
FE = 28 and YZ = 28
Step-by-step explanation:
In similar triangles the ratios of corresponding sides are equal.
(4)
[tex]\frac{BC}{FG}[/tex] = [tex]\frac{BD}{FE}[/tex] , substitute values
[tex]\frac{39}{4x+2}[/tex] = [tex]\frac{42}{5x-2}[/tex] ( cross- multiply )
39(5x - 2) = 42(4x + 2) ← distribute parenthesis on both sides
195x - 78 = 168x + 84 ( subtract 168x from both sides )
27x - 78 = 84 ( add 78 to both sides )
27x = 162 ( divide both sides by 27 )
x = 6
Thus
FE = 5x - 2 = 5(6) - 2 = 30 - 2 = 28
(5)
[tex]\frac{ST}{SZ}[/tex] = [tex]\frac{RT}{YZ}[/tex] , substitute values
[tex]\frac{40}{35}[/tex] = [tex]\frac{3x-7}{2x+2}[/tex] ( cross- multiply )
35(3x - 7) = 40(2x + 2) ← distribute parenthesis on both sides
105x - 245 = 80x + 80 ( subtract 80x from both sides )
25x - 245 = 80 ( add 245 to both sides )
25x = 325 ( divide both sides by 25 )
x = 13
Thus
YZ = 2x + 2 = 2(13) + 2 = 26 + 2 = 28
Following are the solution to the given graph points:
For question 4:
The ratios of equivalent edges of identical triangles are equal (4)
[tex]\to \frac{BC}{FG} = \frac{BD}{FE}[/tex]
Putting given value
[tex]\to \frac{39}{4x+2} = \frac{42}{5x-2}\\\\\to ({39}) ({5x-2}) = ({4x+2}) ({42})\\\\\to 195x -78= 168x+84\\\\\to 195x - 168x=84+78\\\\\to 27x=162\\\\\to x=\frac{162}{27}\\\\\to x=6[/tex]
Therefore,
[tex]\to FE = 5x - 2 = 5(6) - 2 = 30 - 2 = 28[/tex]
For question 6:
[tex]\to \frac{ST}{SZ} = \frac{RT}{YZ}[/tex]
Putting given value
[tex]\to \frac{40}{35} = \frac{3x-7}{2x+2}[/tex]
[tex]\to \frac{40}{35} = \frac{3x-7}{2x+2}\\\\\to 40(2x+2) = (35)(3x-7)\\\\\to 80x +80 = 105x-245 \\\\\to 80+245= 105x-80x\\\\\to 325= 25x\\\\ \to x= \frac{325}{25}\\\\\to x= 13[/tex]
Therefore,
[tex]\to YZ = 2x + 2 = 2(13) + 2 = 26 + 2 = 28[/tex]
Learn more:
brainly.com/question/19817976
