The relationship between the points is an illustration of similar shapes.
The length of AB is 0.43
The given parameters are:
[tex]\mathbf{BE = 1.8}[/tex]
[tex]\mathbf{CD = 9}[/tex]
[tex]\mathbf{BC = 1.7}[/tex]
From the question (see attachment), we have the following observations:
- BE corresponds to CD
- AB corresponds to AC
So, the equivalent ratio is:
[tex]\mathbf{AB:BE =AC:CD }[/tex]
Substitute known values
[tex]\mathbf{AB:1.8 =AC:9 }[/tex]
Express as fractions
[tex]\mathbf{\frac{AB}{1.8} =\frac{AC}{9} }[/tex]
Multiply both sides by 1.8
[tex]\mathbf{AB =\frac{AC}{5} }[/tex]
AC = AB + BC
So, we have:
[tex]\mathbf{AB =\frac{AB + BC}{5} }[/tex]
Substitute 1.7 for BC
[tex]\mathbf{AB =\frac{AB + 1.7}{5} }[/tex]
Multiply through by 5
[tex]\mathbf{5AB =AB + 1.7}[/tex]
Collect like terms
[tex]\mathbf{5AB -AB =1.7}[/tex]
[tex]\mathbf{4AB =1.7}[/tex]
Divide both sides by 4
[tex]\mathbf{AB=0.425}[/tex]
Approximate
[tex]\mathbf{AB=0.43}[/tex]
Hence, the length of AB is 0.43
Read more about similar shapes at:
https://brainly.com/question/20536565
