in the diagram, ab is 6 units, bc is 30 units, and ae is 4 units. if △abe ~ △acd by the sas similarity…

in the diagram, ab is 6 units, bc is 30 units, and ae is 4 units. if △abe ~ △acd by the sas similarity theorem, what is ad? 16 units 20 units 24 units 28 units

in the diagram, ab is 6 units, bc is 30 units, and ae is 4 units. if △abe ~ △acd by the sas similarity theorem, what is ad? 16 units 20 units 24 units 28 units

Answer

Answer:

B. 20 units

Explanation:

Step1: Identify corresponding sides

Since $\triangle ABE\sim\triangle ACD$ by SAS, $\frac{AB}{AC}=\frac{AE}{AD}$.

Step2: Calculate AC

$AC = AB + BC=6 + 30=36$ units.

Step3: Set up proportion

We have $\frac{6}{36}=\frac{4}{AD}$.

Step4: Cross - multiply

$6\times AD=4\times36$.

Step5: Solve for AD

$AD=\frac{4\times36}{6}=20$ units.