Question

HELP PLEASE! FIND THE SCALE FACTOR GIVEN:

Triangle ABC ~ Triangle DEF.
AB=15
BC=Y
AC=18

DE=12
EF=9
DF=X

Answer 1

Given:

`\Delta ABC\sim \Delta D EF`

`AB=15,BC=y,AC=18,DE=12,EF=9,DF=x`

To find:

The values of x and y.

Solution:

We have,

`\Delta ABC\sim \Delta D EF`

Corresponding sides of similar triangles are proportional.

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

On substituting the values, we get

`(15)/(12)=(y)/(9)=(18)/(x)`

`(5)/(4)=(y)/(9)=(18)/(x)`

Now,

`(5)/(4)=(y)/(9)`

`(5)/(4)* 9=(y)/(9)* 9`

`(45)/(4)=y`

`11.25=y`

And

`(5)/(4)=(18)/(x)`

`5* x=18* 4`

`x=(72)/(5)`

`x=14.4`

Therefore, the value of x is 14.4 units and value of y is 11.25 units.