Question

In the map below, the path from the whales to the sharks is parallel to the path from the penguins to the fish tanks. What is the distance between the penguins and the fish tanks?

25 feet
36 feet
69 feet
81 feet

Answer 1

(D) 81feet

Explanation:

From the figure drawn, it is given that AB is parallel to DE, in ΔABC and ΔCDE, we have

∠BAC=∠DEC(Alternate angles)

∠ACB=∠DCE(Vertically opposite angles)

Thus, by AA rule, ΔABC is similar to ΔCDE.

Therefore, using the similarity property, we have

`(CA)/(CE)=(BA)/(DE)`

`(30)/(45)=(54)/(x)`

`x=\frac{54{*}45}{30}`

`x=81feet`

Thus, the distance between the penguins and the fish tanks is 81 feet.

Answer 2

Since the line connecting from the whales to the sharks is parallel to the line connecting from the penguins to the fish tanks, the triangles shown in the figure are similar.

Using the property of similar triangles,

`image`.

The correct choice is the last choice.