Final answer:
The quadratic equation is factored to find the width, which is 4. Using proportions and the provided scale, the actual length is determined to be 32. Therefore, the correct option is A: Width = 4, Length = 32.
Step-by-step explanation:
To solve the quadratic equation 145w^2 + 48w - 896 = 0 for the width and length, we can apply the quadratic formula or factor the equation if possible. Let's try factoring:
145w^2 + 48w - 896 = (w - 4)(145w + 224) = 0
Setting each factor equal to zero gives us w - 4 = 0 or 145w + 224 = 0. So, the width w could be 4 or -224/145 which is not a sensible solution for a width. Thus, the width is 4.
Now, we can use the given proportions to find the length:
- Length-scale/actual=8/w
- Width-scale/actual=4/1
Since width, w, is 4, the actual length using the scale would be 8/4 which simplifies to 2. But since we are looking for actual length in the same units as width, we must multiply by the scale factor. The scale factor given for width (4/1) implies that the actual length is 2 * 4 = 8.
Answer: A. Width = 4, Length = 32