Question

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

Answer:

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

$\frac{AB}{CD} =\frac{BC}{AC} =\frac{AC}{AD}$

now we can take

$\frac{BC}{AC} =\frac{AC}{AD}$

$\frac{4}{AC} =\frac{AC}{9}$     ( since BC=4 and AD= 9)

now we cross multiply

$4(9)=AC^{2}$

$AC^{2}=36$

$AC=\sqrt{36}$    (taking square root )

AC= 6 cm

Answer 2

Answer:

6

Step-by-step explanation: