To solve for the unknown dimensions, we need to identify the correct quadratic equation from the given choices.
The choices provided are:
1. [tex]\( 0 = 2w^2 \)[/tex]
2. [tex]\( 512 = w^2 \)[/tex]
3. [tex]\( 512 = 2w^2 \)[/tex]
4. [tex]\( 512 = 2l + 2w \)[/tex]
Let's analyze them step by step:
1. The equation [tex]\( 0 = 2w^2 \)[/tex] suggests that multiplying 2 by [tex]\( w^2 \)[/tex] results in 0, which implies [tex]\( w \)[/tex] would be 0. Since we are solving for an unknown dimension that results in a specific value (512 in this case), this equation does not suit our requirement.
2. The equation [tex]\( 512 = w^2 \)[/tex] implies that [tex]\( w^2 \)[/tex] equals 512 directly without any consideration of other coefficients or variables. This doesn't fit our scenario where the equation involves a coefficient alongside [tex]\( w^2 \)[/tex].
3. The equation [tex]\( 512 = 2w^2 \)[/tex] appears to be the accurate quadratic equation because it suggests that 512 is twice the value of [tex]\( w^2 \)[/tex]. This fits the requirement as it specifically uses [tex]\( w^2 \)[/tex] multiplied by a coefficient to equal 512.
4. The equation [tex]\( 512 = 2l + 2w \)[/tex] is a linear equation and does not involve a squared term. Hence, it does not represent a quadratic equation suitable for solving for dimensions in this context.
After analyzing each option, the correct quadratic equation to solve for the unknown dimensions is:
[tex]\[ 512 = 2w^2 \][/tex]
