Question

An engineer designs this tower to hold a water tank.

In the diagram, triangles ADE and BCD are similar. What is the length, in feet, of side CD?


Use the on-screen keyboard to type the length of side CD in the box below. Give exact answer.


CD= __ feet

Answer 1

6.75

Explanation:

8÷1.33333....=6

9÷1.33333...=6.75 caz.ADE and BCD are similar.

Answer 2

The length of side CD is 6 2/9 feet.

Since the two triangles are similar, we know that the ratio of the corresponding sides is equal. We can set up the following proportion to find the length of side CD:

`$\frac{CD}{5 \text{ ft}} = \frac{12 \text{ ft}}{9 \text{ ft}}$`

Multiplying both sides of the proportion by 5 ft, we get:

`CD = 5 \text{ ft} \cdot \frac{12 \text{ ft}}{9 \text{ ft}}`

Dividing both sides by 9 ft, we get:

`CD = \frac{5 \text{ ft} \cdot 12 \text{ ft}}{9 \text{ ft}} = (60)/(9) \text{ ft}`

Therefore, the length of side CD is 6 2/9 feet.