Question

part 6 of 6
reject ( x approx -11.5 ) because the measure of a side must be positive.
the width of the rectangle is given by ( x approx square ) yd.
the length of the rectangle is given by ( x + 8 approx square ) yd.

Explanation:

Step1: Determine valid x

Since side length must be positive, we assume the other solution (not -11.5) is positive. Let's assume the equation led to solutions, and we reject -11.5. Suppose the valid x is, for example, if we had a quadratic or other equation, but from the context, likely the positive solution. Wait, maybe the original problem (not shown) had solutions, and we reject -11.5, so the valid x is positive. Let's assume that maybe the other solution is, say, 3.5? Wait, no, maybe the original equation was like x(x + 8) = some area, and solving gave x ≈ -11.5 and x ≈ 3.5 (example). Wait, but since we reject -11.5, the valid x is positive. Let's say the valid x is 3.5? Wait, no, maybe the problem is from a rectangle where length is x + 8, width x, area maybe. But since the user says to reject x ≈ -11.5, the other solution is positive. Let's assume that the valid x is, for example, 3.5? Wait, no, maybe the correct x is 3.5? Wait, no, maybe the original equation was x² + 8x - 40 = 0 (example), solving gives x = [-8 ± √(64 + 160)]/2 = [-8 ± √224]/2 = [-8 ± 4√14]/2 = -4 ± 2√14 ≈ -4 ± 7.483, so x ≈ 3.483 ≈ 3.5 or x ≈ -11.483 ≈ -11.5. So the valid x is ≈ 3.5, then length is 3.5 + 8 = 11.5.

Step2: Calculate length

If x ≈ 3.5, then length is x + 8 ≈ 3.5 + 8 = 11.5.

Answer:

The width of the rectangle is given by \( x \approx \boldsymbol{3.5} \) yd.
The length of the rectangle is given by \( x + 8 \approx \boldsymbol{11.5} \) yd.

(Note: The specific values depend on the original equation, but based on the rejection of -11.5, the positive solution is typically the other root, leading to x ≈ 3.5 and length ≈ 11.5 as a common example. If the original problem had a different equation, adjust accordingly, but this follows the context of rejecting the negative side length.)