Answer:
d
Step-by-step explanation:
Given y is directly proportional to x² then the equation relating them is
y = kx² ← k is the constant of proportion
To find k use the condition y = 
when x = 
, then
= k( )² = 
k ( multiply both sides by 8 )
1 = 2k ( divide both sides by 2 )
k =
y = x² ← equation of proportion
When y = 
, then
= x² ( multiply both sides by 2 )
9 = x² ( take the square root of both sides )
x = ± 
= ± 3
with positive value x = 3 → d
You had the right idea using the Pythagorean theorem to solve for b.
Problem is for that triangle to work, the 5 and the 2√2 would have to switch places. The length of a leg cannot be larger than the length of the hypotenuse for it to truly be a right triangle.
Pythagorean theorem only works for the right triangles. Only way to "solve this problem would be to bring in complex numbers.
5² + b² = (2√2)²
25 + b² = 2²(√2)²
25 + b² = 4(2)
25 + b² = 8
b² = 8 - 25
b² = - 17
b = √-17
b= (√17i)
Then the problem with THIS is a measurement/distance cannot be negative... which goes against exactly what that complex number i is.
I do believe the answer is D
