Question

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Answer 1

`x=16(28)/(37)\\ \\y=5(1)/(3)\\ \\z=7.5`

Explanation:

The diagram shows three paralel lines which divide the large triangle into three similar triangles.

By Thales theorem,

`(5)/(z)=(y)/(8)=(2)/(3)`

Then

`(5)/(z)=(2)/(3)\Rightarrow 2z=15,\ z=7.5\\ \\(y)/(8)=(2)/(3)\Rightarrow 3y=16,\ y=(16)/(3)=5(1)/(3)`

From the similarity of triangles,

`(x)/(20)=(z+8)/(z+8+3)\\ \\(x)/(20)=(7.5+8)/(7.5+8+3)\\ \\(x)/(20)=(15.5)/(18.5)\\ \\x=20\cdot (155)/(185)=20\cdot (31)/(37)=(620)/(37)=16(28)/(37)`