To solve this problem, you need to evaluate whether each option forms a golden rectangle given the area of 135 square inches. A golden rectangle is one where the ratio of the longer side to the shorter side approximates the golden ratio, which is approximately 1.618. Also, the product of the dimensions should equal the given area.
1. Define the Golden Ratio:
[tex]\[
\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618
\][/tex]
2. Check Each Option:
- Option A: [tex]\(16 \times 8\)[/tex]
- Area: [tex]\(16 \times 8 = 128\)[/tex]
- Area does not match [tex]\(135 \text{ in}^2\)[/tex].
- Option B: [tex]\(9 \times 15\)[/tex]
- Area: [tex]\(9 \times 15 = 135\)[/tex]
- Area matches [tex]\(135 \text{ in}^2\)[/tex].
- Ratio: [tex]\( \frac{15}{9} \approx 1.667\)[/tex]
- The ratio [tex]\(1.667\)[/tex] is close to the golden ratio [tex]\(1.618\)[/tex].
- Option C: [tex]\(10 \times 14\)[/tex]
- Area: [tex]\(10 \times 14 = 140\)[/tex]
- Area does not match [tex]\(135 \text{ in}^2\)[/tex].
- Option D: [tex]\(11 \times 13\)[/tex]
- Area: [tex]\(11 \times 13 = 143\)[/tex]
- Area does not match [tex]\(135 \text{ in}^2\)[/tex].
3. Conclusion:
- Only Option B ([tex]\(9 \times 15\)[/tex]) has the correct area and a ratio closest to the golden ratio.
Thus, the correct answer is B.
