Question

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

Explanation:

Step1: Find AC

Since \(AC = AB+BC\), and \(AB = 6\), \(BC = 30\), then \(AC=6 + 30=36\).

Step2: Use SAS similarity ratio

Because \(\triangle ABE\sim\triangle ACD\) by SAS similarity theorem, we have \(\frac{AB}{AC}=\frac{AE}{AD}\).
Substitute \(AB = 6\), \(AC = 36\), \(AE = 4\) into \(\frac{AB}{AC}=\frac{AE}{AD}\), we get \(\frac{6}{36}=\frac{4}{AD}\).
Cross - multiply: \(6\times AD=36\times4\).
Then \(AD=\frac{36\times4}{6}\).
Calculate \(36\times4 = 144\), and \(144\div6 = 24\).

Answer:

24 units