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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.

Sagot :

MrRoyal

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

View image MrRoyal
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