Question

Can someone help me on this?

Answer 1

Given:

`\Delta DE F\sim \Delta DST`

`DE=40, EF=4x-4,DS=10,ST=11`

To find:

The value of x.

Solution:

We have,

`\Delta DE F\sim \Delta DST`

The corresponding sides of the similar triangles are proportional.

`(DE)/(DS)=(EF)/(ST)`

On substituting the given values, we get

`(40)/(10)=(4x-4)/(11)`

`4=(4x-4)/(11)`

Multiply both sides by 11.

`4* 11=4x-4`

`44=4x-4`

Add 4 on both sides.

`44+4=4x`

`48=4x`

Divide both sides by 4.

`(48)/(4)=x`

`12=x`

The value of x is 12. Therefore, the correct option is D.