I need answers please. Fiona wants to rope off a triangular region in her yard for a vegetable garden. She has 90 feet of rope to use, she wants the distance between each stake to be an integer, and the distance between two of the stakes must be 36 feet.

1. What is the greatest possible distance between any of the stakes?

2. If she wants to create a right triangular region and use all of the 90 feet of rope, what would be the lengths of the sides of the region?

Problem 1

Let's say that c = 36.  

Since she has 90 feet of rope total, that leaves 90-36 = 54 feet of rope for sides 'a' and b to divide up somehow. We can say a+b = 54  

Now let's say we want 'a' to be as large as possible. To do this, we need to make b as small as possible. That occurs when b = 1. We can't have b = 0, or else a triangle won't form. So the next value up is b = 1.  

If b = 1, then,

a+b = 54

a = 54-b

a = 54-1

a = 53

The longest side possible is 53 feet

Problem 2

Recall that (5,12,13) is a pythagorean triple. This is because 5^2+12^2 = 13^2. Both sides lead to 169.

Since we have a pythagorean triple, this indicates a triangle with sides 5,12,13 is a right triangle.

If a triangle has sides 5,12, and 13, then the perimeter is 5+12+13 = 30.

Triple each side to get a larger triangle of 15, 36, and 39. The larger perimeter is 90 after adding those larger sides. Note the jump from 30 to 90 is "times 3". It's not a coincidence that the perimeter has multiplied by the same scale factor as the side lengths.

Also note that 15^2+36^2 = 39^2. Both sides lead to 1521. This indicates we have a right triangle and (15,36,39) is another pythagorean triple. Any scaled version of a pythagorean triple, is also a pythagorean triple.

In short, we've found that a triangle with sides 15, 36, and 39 is a right triangle and has perimeter 90 feet.

answer:

3 bags of apples and 2 bags of oranges.

step-by-step explanation: