Question

If ABC ~ DEF and the scale factor from ABC to DEF is 1/7, what are the lengths of DE, EF, and DF respectively?

Answer 1

452

Step-by-step explanation:

Answer 2

Option D is correct.

The length of segment DE = 4 unit ,

Length of segment EF = 5 unit

Length of segment DF = 2 unit

Step-by-step explanation:

Given:

If Δ ABC
`\sim` Δ DEF and the scale factor from ABC to DEF is
`(1)/(7)`

We know that:

Scale factor=measure triangle DEF/measure triangle ABC

then,

`(DE)/(AB) =k` ,
`(DF)/(AC) =k` , and
`(EF)/(BC) =k`

Scale factor (k) =
`(1)/(7)`

From the figure; we have

length of segment AB = 28 unit

length of segment AC = 14 unit

Length of segment BC = 35 unit

Then,

*
`(DE)/(28) =(1)/(7)`

or

`DE = (1)/(7) * 28 = 4 unit`

*
`(DF)/(14) =(1)/(7)`

or

`DF = (1)/(7) * 14 = 2 unit`

*
`(EF)/(35) =(1)/(7)`

or

`EF = (1)/(7) * 35 = 5 unit`

Therefore, the length of segment DE , EF and DF are; 4 unit, 5 unit , and 2 unit.