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

Triangle ABC is similar to triangle DEC. If AC measures 30 inches then what is the-example-1
User Ekenman
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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.

User Bourbon
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