right triangle ABC with right angle C, AC=22 and BC=6, altitude CD where D is on hypotenuse AB. What is the ratio of the area of triangle ADC to the area of triangle CDB? Write ratio as n:1 and round n to the nearest hundredth.

Question

right triangle ABC with right angle C, AC=22 and BC=6, altitude CD where D is on hypotenuse AB.  What is the ratio of the area of triangle ADC to the area of triangle CDB? Write ratio as n:1 and round n to the nearest hundredth.

Reiny · Answer

Mark you similar triangles filling in all given information
I see
triangle ADC similar to
triangle CDB

The ratio of areas of two triangles is equal to the squares on their corresponding sides.

Triangle ADC : triangle CDB = (CA)^2 : (BC)^2
= 22^2 : 6^2
= 484 : 36
= 121 : 9
or (121/9) : 1

n = 121/9 or 13 4/9 or 13.44444.....