Pythagorean triplet whose one member is 15

Step-by-step explanation:

If

for m > n, then a, b, c make a Pythagorean triplet.

We have the system of equations:

Substitute to the second equation:

Therefore we have:

 it's impossible, because 15 is not an even number.

Let's consider all possible sums of two numbers resulting in 15.

We will check which of the numbers are perfect squares.

1 + 14

2 + 13

3 + 12

4 + 11

5 + 10

6 + 9

7 + 8

(Bold not perfect squares)

There are no two perfect squares among the listed pairs of numbers.

Other:

15, 112, 113

We know the Egyptian triangle with sides of length 3, 4, 5.

By modifying this Pythagorean triplet by multiplying by 3 we get:

(3)(3) = 9; (3)(4) = 12; (3)(5) = 15

By modifying this Pythagorean triplet by multiplying by 5 we get:

(5)(3) = 15; (5)(4) = 20; (5)(5) = 25

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

your answer is

a.

5

step-by-step explanation: