Question

joel wants to fence off a triangular portion of his yard for his chickens. the three pieces of fencing he has measure 8 feet, 15 feet, and 20 feet long. use this information to answer 7-9.

1. will joel be able to make a right triangle with the current lengths of fencing? why or why not?
2. joel cut the longest piece of fencing in order to make a right triangle. find the perimeter of joel’s fence.
3. if it takes joel 30 seconds to install each foot of fencing, how many total minutes will it take him to install the fence?

Explanation:

Step1: Check right triangle condition

For a right triangle, the Pythagorean theorem must hold: $a^2 + b^2 = c^2$, where $c$ is the longest side.
Calculate $8^2 + 15^2 = 64 + 225 = 289$
Calculate $20^2 = 400$
Since $289
eq 400$, the sides do not satisfy the theorem.

Step2: Find new right triangle sides

We keep 8 ft and 15 ft as the legs of the right triangle. Calculate the required hypotenuse $c$:
$c = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17$ ft
Perimeter = $8 + 15 + 17 = 40$ ft

Step3: Calculate total installation time

First, find total length of original fencing: $8 + 15 + 20 = 43$ ft
Total time in seconds: $43 \times 30 = 1290$ seconds
Convert to minutes: $\frac{1290}{60} = 21.5$ minutes

Answer:

1. No, because the side lengths do not satisfy the Pythagorean theorem: $8^2 + 15^2

eq 20^2$.

1. 40 feet
2. 21.5 minutes