Question

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

Explanation:

Step1: Calculate AC length

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

Step2: Set up similarity ratio

By SAS similarity, $\frac{AB}{AC} = \frac{AE}{AD}$
$\frac{6}{36} = \frac{4}{AD}$
Simplify: $\frac{1}{6} = \frac{4}{AD}$
Solve for AD: $AD = 4×6 = 24$ units

Answer:

C. 24 units