Final answer:
To find the area of the enlarged rectangle with a width of 15 inches, we determine the scale factor to be 2.5 and enlarge both the width and length by this factor, resulting in an area of 300 square inches.
Step-by-step explanation:
The question asks to find the area of Nurbanu's enlarged rectangular design that is now 15 inches wide. The original rectangle has an area of 48 square inches and a width of 6 inches. To find the length of the original rectangle, we divide the area by the width, thus 48 square inches ÷ 6 inches equals 8 inches in length.
Since the width of the enlarged design is 15 inches, and the original width is 6 inches, we can determine the scale factor, which is 15 inches ÷ 6 inches, equalling a scale factor of 2.5. To find the area of the enlarged design, we must apply the scale factor to both the width and the length of the original rectangle.
This means the length will also be scaled by 2.5 times, so the new length will be 8 inches × 2.5, which equals 20 inches. Hence, the area of the enlarged design will be 15 inches × 20 inches, equaling 300 square inches.