Question

Given: ABC ||| EDF

Calculate the length of AB

Answer 1

AB = 9 cm

Explanation:

Δ ABC and Δ EDF are similar triangles

The ratios of corresponding sides are in proportion

corresponding sides are

AB and ED , BC and DF , AC and EF , then

`(AB)/(ED)` =
`(BC)/(DF)` ( substitute values )

`(AB)/(6)` =
`(15)/(10)` ( cross- multiply )

10 AB = 6 × 15 = 90 ( divide both sides by 10 )

AB = 9 cm

Answer 2

AB = 22.5 cm

Explanation:

The notation ΔABC ||| ΔEDF indicates that the triangles ABC and DEF are parallel. In geometry, when two triangles are denoted as parallel, it means that their corresponding sides are parallel, and their corresponding angles are congruent. Therefore, the two triangles are similar.

In similar triangles, corresponding sides are in the same ratio. Therefore:

`AB:BC=DE:EF`

Given than BC = 15 cm, DE = 6 cm and EF = 4 cm, then:

`AB:15=6:4`

Solve for AB:

`(AB)/(15)=(6)/(4)`

`(AB)/(15)* 15=(6)/(4)* 15`

`AB=22.5`

So, the length of AB is 22.5 cm.