Bill runs diagonally across a rectangular field that has a length of 24 yards and a width of
32 yards. What is the length of the diagonal, in yards that Bill runs?

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)