Question

isosceles △abc (ac = bc) has base angles of 30° and cd is the median to base. how long are the legs of △abc, if the sum of the perimeters of △acd and △bcd is 20 cm more than the perimeter of △abc?

Explanation:

Step1: Analyze perimeters

Since CD is median to base AB in isosceles △ABC (AC = BC), perimeter of △ACD+△BCD - perimeter of △ABC = 2CD. Given this is 20 cm, so CD = 10 cm.

Step2: Use angle - side relationship

In right - triangle ACD (∠A = 30°), AC = 2CD.
AC = 2×10 = 20 cm.

Answer:

20