Question

Use the information below to find EF such that ABC ~ DEF. AB = 36, BC = 24, DE = 48, B= 110 angle E = 110 angle, EF = ? A.32 B.36 C.68 D.72

Answer 1

The first thing we are going to do, is draw our triangles (picture 1).
Since both triangles must be similar, the ratios of the lengths of their corresponding sides must be equal.
We can infer from our picture that the segment AB is corresponding to the segment DE and the segment BC is corresponding to the segment EF, so lets find the ratios of those corresponding sides and establish a proportion to find the length of EF:

`(AB)/(DE) = (BC)/(EF)`
We know from our problem that
`AB=36`,
`BC=24`, and
`DE=48`, so lets replace those values in our proportion:

`(36)/(48) = (24)/(EF)`

`EF= (48*24)/(36)`

`EF=32`

We can conclude that the length of EF, such that ABC ~ DEF, is 10 units.

Answer 2

Correct option is A) 32

Explanation:

In figure-1 , the triangle Δ ABC and Δ DEF

Since, both triangles are similar then ratios of their lengths of corresponding sides must be equal.

`(AB)/(DE)=(BC)/(EF)`

`(36)/(48)=(24)/(EF)`

Simplify the above,

`(36)/(48)=(24)/(EF)`

Multiply both the sides by
`(EF)/(24)`

`(EF)/(24)*(36)/(48)=(EF)/(24)* (24)/(EF)`

`(EF)/(2)*(1)/(16)=1`

`(EF)/(32)=1`

multiply both sides by '32' on both the sides of above expression,

`EF=32`

Hence, correct option is A) 32