Given:
[tex]\Delta DE F\sim \Delta DST[/tex]
[tex]DE=40, EF=4x-4,DS=10,ST=11[/tex]
To find:
The value of x.
Solution:
We have,
[tex]\Delta DE F\sim \Delta DST[/tex]
The corresponding sides of the similar triangles are proportional.
[tex]\dfrac{DE}{DS}=\dfrac{EF}{ST}[/tex]
On substituting the given values, we get
[tex]\dfrac{40}{10}=\dfrac{4x-4}{11}[/tex]
[tex]4=\dfrac{4x-4}{11}[/tex]
Multiply both sides by 11.
[tex]4\times 11=4x-4[/tex]
[tex]44=4x-4[/tex]
Add 4 on both sides.
[tex]44+4=4x[/tex]
[tex]48=4x[/tex]
Divide both sides by 4.
[tex]\dfrac{48}{4}=x[/tex]
[tex]12=x[/tex]
The value of x is 12. Therefore, the correct option is D.
