Question

PLEASE HELP!!

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.

Answer 1

6 cm

Explanation:

Let k represent the scale factor between ΔABC and ΔDCA. Then ...

... CA = k·BC

... AD = k·CA

So, AD/BC = k·(k·BC)/BC = k² = 9/4

Then k = √(9/4) = 3/2, and ...

... CA = (3/2)·BC = (3/2)·(4 cm)

... CA = 6 cm