If \( A \propto B^{2} \), and \( A=45 \) whe \( B=3 \), find \( B \) when \( A=80 \)

Let's first express the relationship \( A \propto B^{2} \) as an equation: \[ A = kB^{2} \] where \( k \) is a constant. Given that \( A = 45 \) when \( B = 3 \), we can find \( k \): \[ 45 = k(3^{2}) \] This simplifies to: \[ 45 = 9k \] Now, solving for \( k \): \[ k = \frac{45}{9} = 5 \] Now we have the equation: \[ A = 5B^{2} \] Next, we want to find \( B \) when \( A = 80 \): \[ 80 = 5B^{2} \] Dividing both sides by 5: \[ 16 = B^{2} \] Taking the square root of both sides gives us: \[ B = 4 \] So, when \( A = 80 \), \( B = 4 \).