Question

Triangle ABC is similar to triangle DEC. If AC measures 30 inches then what is the length of AD?

Answer 1

The length of AD is 20 inches.

If triangle ABC is similar to triangle DEC, it means that the corresponding sides are in proportion. In other words:

`(AB)/(DE) =(AC)/(DC)`

You provided the values:

AB=18cm

DE=6in

AC=30in

Let's denote the length of DC as x (in inches). Now we can set up the proportion:

18/ 6=30/X

​Now, we can cross-multiply to solve for x:

18x=30×6

18x=180

x= 180/ 18

x=10

So, the length of DC is 10 inches. Now, since AD is a part of side AC, you can find the length of AD by subtracting the length of DC from the length of AC:

AD=AC−DC

AD=30−10

AD=20

Therefore, the length of AD is 20 inches.