Diagonal ac divides the trapezoid abcd (with bases ad and bc , ad> bc) into two similar triangles, △abc and △dca. find ac if bc=4 cm and ad=9 cm.

AC= 6 cm

Step-by-step explanation:

It is given that ABCD is a trapezoid

Also AC divides the trapezoid into two similar triangles

ΔABC≈ΔDCA

The ratio of corresponding sides of similar triangles are equal, so we have

now we can take

    ( since BC=4 and AD= 9)

now we cross multiply

   (taking square root )

AC= 6 cm