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Lubov Fominskaja [6]
2 years ago
15

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 th

e length of AB.Write your answer to two decimal places.
Mathematics
1 answer:
katrin2010 [14]2 years ago
7 0

The relationship between the points is an illustration of similar shapes.

The length of AB is 0.43

The given parameters are:

\mathbf{BE = 1.8}

\mathbf{CD = 9}

\mathbf{BC = 1.7}

From the question (see attachment), we have the following observations:

  • BE corresponds to CD
  • AB corresponds to AC

So, the equivalent ratio is:

\mathbf{AB:BE =AC:CD }

Substitute known values

\mathbf{AB:1.8 =AC:9 }

Express as fractions

\mathbf{\frac{AB}{1.8} =\frac{AC}{9} }

Multiply both sides by 1.8

\mathbf{AB =\frac{AC}{5} }

<em>AC = AB + BC</em>

So, we have:

\mathbf{AB =\frac{AB  + BC}{5} }

Substitute 1.7 for BC

\mathbf{AB =\frac{AB  + 1.7}{5} }

Multiply through by 5

\mathbf{5AB =AB  + 1.7}

Collect like terms

\mathbf{5AB -AB  =1.7}

\mathbf{4AB  =1.7}

Divide both sides by 4

\mathbf{AB=0.425}

Approximate

\mathbf{AB=0.43}

Hence, the length of AB is 0.43

Read more about similar shapes at:

brainly.com/question/20536565

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