A, B and C lie on a straight line segment.A, E and D lie on a straight line segment.BE = 1.8m, CD = 9m and BC = 1.7m.Work out the length of AB.Write your answer to two decimal places.
Answers
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 CDAB corresponds to ACSo, 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
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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