Question

In the diagram, triangle ACE is similar to triangle DCB. Find the length of line AB.
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Answer 1

AB = 18

Explanation:

given Δ ACE and Δ DCB are similar , then the ratios of corresponding sides are in proportion.

corresponding sides are

AC and DC , CE and CB , AE and DB , then

`(AC)/(DC)` =
`(CE)/(CB)` ( substitute values )

note that AC = AB + BC = AB + 10

`(AB+10)/(14)` =
`(14+6)/(10)` =
`(20)/(10)` ( cross- multiply )

10(AB + 10) = 14 × 20 = 280 ( divide both sides by 10 )

AB + 10 = 28 ( subtract 10 from both sides )

AB = 18