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: Find AC length

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

Step2: Set up proportion for similar triangles

Since \(\triangle ABE \sim \triangle ACD\) (SAS similarity), the ratios of corresponding sides are equal. So \(\frac{AB}{AC} = \frac{AE}{AD}\).

Step3: Substitute values and solve for AD

Substitute AB = 6, AC = 36, AE = 4 into the proportion: \(\frac{6}{36} = \frac{4}{AD}\). Cross - multiply: \(6\times AD = 36\times4\). Then \(AD=\frac{36\times4}{6}\). Calculate \(36\div6 = 6\), and \(6\times4 = 24\).

Answer:

24 units (corresponding to the option "24 units")