Question

Joel wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has to use are 15 feet, 8 feet, and 20 feet long.

1. Will he be able to make a right triangle out of his fence? Why or why not?

2. Joel cut the longest piece of wood in order to make a right triangle. If it takes him 30 seconds to install each foot of fencing, how many total minutes will it take him to install all of the fence?

Answer 1

20

Explanation:

Answer 2

Answer: He needs 20 minutes to install all of the fence.

Explanation:

Since we have given that

Dimensions of triangle he has to use for fencing are

15 feet, 8 feet, and 20 feet.

1) For making it a right triangle it must satisfy the "Pythagorus theorem" which states that

`H^2=B^2+P^2\\\\20^2=15^+8^2\\\\400\\eq 225+64\\\\400\\eq 289`

No, it will not be able to make a right triangle.

2) Joel cut the longest piece of wood in order to make a right triangle.

So, from above we get that

`√(289)=17\ feet`

So, Longest side must be 17 feet.

It is takes him 30 seconds to install each foot of fencing,

Total perimeter of fencing will be

`17+15+8=40\ feet`

So, for 1 foot he needs = 30 seconds

For 40 feet , he will need

`40* 30=1200\ seconds\\\\(1200)/(60)=20\ minutes`

Hence, he needs 20 minutes to install all of the fence.