Question

What is the length of DE?

Answer 1

Hi!

So we need to know how much smaller ΔDEF is than ΔABC.

See line DF compared to AC. PQ is 1.5 times smaller than DF. That means ΔDEF is 1.5 times smaller than ΔABC.

So to find the length of DE, divide AB by 1.5.

27/1.5 = 18

x=18

The length of DE is 18

Hope this helps! :)

-Peredhel

Answer 2

Hello!

These are similar triangles. As you can see, they have the same angle and all corresponding side lengths have the same ratio.

As you can see, the length of AC appears to be 3/2 of DF, it's corresponding side. This means that x is 2/3 of 27.

2/3(27)=18

Therefore, our answer is D) 18.

I hope this helps!