Answer:
Perimeter=42cm
Step-by-step explanation:
It is given that AC is the angle bisector of the trapezoid ABCD which divides the trapezoid into two similar triangles that are △ABC and △ACD.
Now, it is also given that AB=9cm and CD=12cm.
Since, it is a trapezoid, then AB will be parallel to CD, thus
∠BAC=∠DCA (Alternate angles)
Also, it is given that ∠DAC=∠BAC
⇒∠DAC=∠DCA
Also, ∠ACD=∠ACB( Angle bisector)
Therefore, If the angles are equal, then the corresponding sides will also be equal. Hence, △ABC and △ACD are isosceles triangle, therefore
AB=BC=9cm and CD=AD=12cm
Now, the perimeter of trapezoid is the sum of all the four sides of the trapezoid, therefore
Perimeter=AB+AD+CD+BC
Perimeter=9+9+12+12
Perimeter=42cm
