Question

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.

Answer 1

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

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

AC = AB + BC

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