In the diagram:
AB is parallel to ED,
the points B, C and E lie on a straight line, and
the points A, C and D also lie on a straight line.
What is the value of e (the length of CD) ?

14.5

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16.5

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17.5

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Solution

The correct option is B 16.5
Angle BCA = Angle DCE
And since AB and ED are parallel,
Angle ABC = Angle DEC and
Angle BAC = Angle EDC
So the two triangles have exactly the same angles and are therefore similar triangles.
Next, find the scale factor
= $\frac{D E}{A B} = \frac{10.5}{7} = 1.5$
Therefore, $C D = 1.5 \times A C = 1.5 \times 11 = 16.5$

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In the diagram:AB is parallel to ED,the points B, C and E lie on a straight line, andthe points A, C and D also lie on a straight line.What is the value of e (the length of CD) ?

The correct option is B 16.5Angle BCA = Angle DCE And since AB and ED are parallel,Angle ABC = Angle DEC andAngle BAC = Angle EDCSo the two triangles have exactly the same angles and are therefore similar triangles.Next, find the scale factor=DEAB=10.57=1.5Therefore, CD=1.5×AC=1.5×11=16.5

In the diagram:
AB is parallel to ED,
the points B, C and E lie on a straight line, and
the points A, C and D also lie on a straight line.
What is the value of e (the length of CD) ?