Asap plz 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.

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