Final answer:
To create a scaled copy of a rectangle with an original size of 3 units by 5 units that has an area of 60 square units, we find a scale factor which is the square root of the ratio of the new area to the original 15 units (√(60/15) = 2). By scaling each dimension by this factor, we get a new rectangle that is 6 units by 10 units, which is answer B).
Step-by-step explanation:
The question asks us to sketch a scaled copy of a rectangle with an original size of 3 units by 5 units that has an area of 60 square units. To create a scaled copy with the same shape (proportions), we need to maintain the aspect ratio of the original rectangle while adjusting the size to achieve the new area.
We calculate the area of rectangle S by multiplying its length and width: 3 units × 5 units = 15 square units. To find the scaled dimensions that will give us an area of 60 square units, we can use a scale factor. The scale factor is the square root of the ratio of the new area to the original area, which is √(60/15) = √4 = 2. Therefore, we need to multiply each dimension of rectangle S by 2 to get a rectangle with an area of 60 square units.
If we double the dimensions of rectangle S, we get a new rectangle that is 6 units by 10 units, which has an area of 6 units × 10 units = 60 square units. This rectangle is a scaled copy of rectangle S with the required area. Therefore, the answer is B) 6 units by 10 units.