Question

1. Steve is turning half of his backyard into a chicken pen. His backyard is a 24 meter by 45 meter rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. How many meters of fencing will Steve need?

2. Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it. The mail slot is 7 cm wide by 24 cm long. The widest part of the slot occurs across the diagonal of the mail slot. What is the maximum width of the mail slot?
3. Meg lives in Indianapolis and wants to visit her mom in Lima, which is 173 miles Northeast of Indianapolis. Dayton is 165 miles directly East of Indianapolis. How many more kilometers would Meg drive if she drove to Lima through Dayton?
4. Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square of white flag with sides of 12 centimeters. He will make the "X" by stretching red ribbon diagonally from corner to corner. How many centimeters of ribbon will Peter need to make the "X"?

Answer 1

1. Steve will need approximately 60 meters of fencing for the chicken pen.

2. The maximum width of the mail slot is approximately 25 cm.

3. Meg would drive approximately 200 kilometers more if she drove to Lima through Dayton.

4. Peter will need approximately 16.97 centimeters of ribbon to make the "X" on the flag.

Step-by-step explanation:

1. Steve will need approximately 60 meters of fencing for the chicken pen.

To find the length of the diagonal (the fencing needed) in Steve's rectangular backyard, we can use the Pythagorean theorem. Considering a 24 by 45 meter rectangle, the diagonal (D) can be calculated as follows: (
`D = √(24^2 + 45^2)`). Solving this yields approximately 52.2 meters. However, Steve needs fencing on both sides of the diagonal, so we double this value, resulting in approximately 104.4 meters. As the question asks for half the backyard, the final answer is approximately 52.2 meters.

2. The maximum width of the mail slot is approximately 25 cm.

Utilizing the Pythagorean theorem, we find the diagonal (D) of the mail slot with dimensions 7 cm by 24 cm: (
`D = √(7^2 + 24^2)`). Solving this yields approximately 25.3 cm, which represents the maximum width of the mail slot.

3. Meg would drive approximately 200 kilometers more if she drove to Lima through Dayton.

The additional distance driven is the difference between the direct distances to Lima and the combined distances to Dayton and Lima, which can be calculated as 173 - (165 + 173) , resulting in approximately 200 kilometers.

4. Peter will need approximately 16.97 centimeters of ribbon to make the "X" on the flag.

Calculating the ribbon length for the diagonal of the square flag (X) using the Pythagorean theorem (
`\( X = √(12^2 + 12^2) \)`) yields approximately 16.97 centimeters.