In trapezoid ABCD, base BC = 12 cm, diagonal AC = 24 cm and angle BAC = angle ADC. Find the base AD.

univerkov | September 11, 2021 | education

The AC diagonal divides the trapezoid into two similar triangles ABC and ABC. Triangles are similar in two angles, since the angle BAC = ADC by condition, and the angle ACB = CAD as lying cross at the intersection of parallel straight lines.

Then the aspect ratio in similar triangles is:

BC / AC = AC / AD.

AD = AC * AC / BC = 24 * 24/12 = 48 cm.

Answer: The length of the base AD is 48 cm.

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