Question

ABC and AED are straight lines.

BE and CD are parallel.
A
B
AD = 10.5 cm
AE = 4.2 cm
BE = 2.9 cm
a) Work out length CD.
AC = 8.75 cm
b) Work out length BC.

Answer 1

a) CD = 7.25

b) BC = 5.25

Explanation:

a)

The parallel lines mean the triangles are similar. ΔADC ~ ΔAEB. Corresponding sides are proportional, so ...

AD/AE = DC/EB

10.5/4.2 = CD/2.9

CD = 2.9(5/2) = 7.25

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b)

Corresponding sides are proportional, so ...

BC/AC = ED/AD

BC = AC(ED/AD) = 8.75(10.5 -4.2)/10.5 = 8.75(3/5) = 5.25