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.

$\dfrac{DE}{DS}=\dfrac{EF}{ST}$

On substituting the given values, we get

$\dfrac{40}{10}=\dfrac{4x-4}{11}$

$4=\dfrac{4x-4}{11}$

Multiply both sides by 11.

$4\times 11=4x-4$

$44=4x-4$

Add 4 on both sides.

$44+4=4x$

$48=4x$

Divide both sides by 4.

$\dfrac{48}{4}=x$

$12=x$

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