Use the image to answer the question.

Question

Two boats are drawn on a 14 by 15 grid. A small boat on the left is labeled A, and a bigger boat to the right is labeled B. A diagonal dashed line extends downward from boat A, and intersects with a vertical downward line from boat B, creating two triangles.

Given that AB¯¯¯¯¯¯¯¯ =9 units in length and BC¯¯¯¯¯¯¯¯=12 units in length, how many units is CE¯¯¯¯¯¯¯¯ ?

(1 point)
Responses

21
21

6
6

24
24

15

Answer 1

To solve for \( CE \) in the given scenario, we start by using the lengths provided in the problem.

1. We know:

   • \( AB = 9 \) units
   • \( BC = 12 \) units

2. The two triangles created by the boats and the dashed line consist of:

   • Triangle \( ABE \) with base \( AB \) and height \( CE \)
   • Triangle \( BCD \) with base \( BC \) and height \( CE \)

By observing the setup, we notice that since the dashed line is perpendicular to the lines from the boats (assuming a right angle setup at E), we can utilize similar triangles or basic relationships between the segments:

The total length from A to C, which is \( AC \), is the sum of \( AB + BC \): \[ AC = AB + BC = 9 + 12 = 21 \text{ units} \]

If \( CE \) represents the height of both triangles and we know that the total from A down to C follows the lines and segments given:

Thus, the length \( CE \) can be directly inferred as the height connecting the points of intersection:

From the total distances available and splitting them: \[ CE = AC = 21 \text{ units} \]

Therefore, the answer is: \[ \boxed{21} \]