Tommy has a bird feeder in the corner of his yard and is paving a path between the feeder and his patio. A diagram of Tommy's yard is shown below.

A rectangle with length 28 feet and width 20 feet has a bird feeder in the top left corner. The square patio with side length 9 feet is at right bottom corner of the rectangle. top left corners joined by a dotted line labeled path.

What is the length of the path, to the nearest foot?

A.
22 feet

B.
25 feet

C.
30 feet

D.
34 feet

1 answer

To find the length of the path from the bird feeder in the top left corner of Tommy's yard to the patio in the bottom right corner, we can start by determining the coordinates of both points.

  1. The bird feeder is at the top left corner of a rectangle, so its coordinates are (0, 0).
  2. The bottom right corner of the rectangular yard is (28, 20) since it has a length of 28 feet and a width of 20 feet.
  3. The square patio is at the bottom right corner of the rectangle, but it occupies a 9 feet by 9 feet area. Thus, the top left corner of the patio would be at (28 - 9, 20 - 9) = (19, 11).

Now, we need to find the straight line distance (the path) from the point (0, 0) (the bird feeder) to the point (19, 11) (the top left corner of the patio). This can be calculated using the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting in the coordinates:

\[ d = \sqrt{(19 - 0)^2 + (11 - 0)^2} = \sqrt{19^2 + 11^2} \]

Calculating further:

\[ d = \sqrt{361 + 121} = \sqrt{482} \]

Next, we can approximate \(\sqrt{482}\).

Calculating it gives:

\[ \sqrt{482} \approx 22 \]

Now rounding this to the nearest foot, we get:

The nearest foot value for the length of the path is 22 feet.

Thus, the answer is A. 22 feet.