Question

If ?ABE is similar to ?ACD by the SAS similarity theorem, AD must equal how many units.

Answer 1

the correct answer for this on edg. is 24

Answer 2

Answer: 24 units

Step-by-step explanation:

Given: Δ ABE is similar to Δ ACD by the SAS similarity theorem.

Since the corresponding sides of similar triangles are proportional.

Therefore we have

$\frac{AB}{AC}=\frac{AE}{AD}\\\\\Rightarrow\frac{AB}{AB+BC}=\frac{AE}{AE+ED}\\\\\Rightarrow\frac{6}{6+30}=\frac{4}{AD}\\\\\Rightarrow\ AD=\frac{4\times36}{6}\\\\\Rightarrow\ AD=24$

Hence, if Δ ABE is similar to Δ ACD by the SAS similarity theorem then AD must equal 24 units.