This problem is only for smart kids, all people who dont do it r babies an angle bisector ac divides a trapezoid abcd into two similar triangles △abc and △acd. find the perimeter of this trapezoid if the leg ab=9 cm and the leg cd=12 cm.

46

Step-by-step explanation:

∠DAC ≅ ∠ACB because they are opposite interior angles where transversal AC crosses parallel lines BC and AD.

∠DAC ≅ ∠CAB because they are corresponding angles of the similar triangles ΔABC and ΔACD.

Hence ∠ACB ≅ ∠CAB and ΔABC is isosceles with side lengths both being 9. The corresponding side lengths of ΔACD are 12, meaning the base of ΔABC, segment AC, is 12. The scale factor of ΔACD to ΔABC is then 12:9 = 4:3, so the base AD of ΔACD is (4/3)×12 = 16.

So, the side lengths of the trapezoid are ...

and the perimeter is 9 +9 +12 +16 = 46 units.

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