Final answer:
Tina will need to trim her photo to approximately 8.5 inches by 11.3 inches in order to reduce the area to half of the original size, while maintaining the shape proportions.
Step-by-step explanation:
Tina bought a 12 inches by 16 inches photo that she needs to reduce in size so that the area is halved. To solve for the dimensions of a smaller photo with half the original area, we can use the concept of scale factors and the relationship between area and side lengths of a rectangle.
The original area is 12 inches × 16 inches = 192 square inches. Halving the area gives us 96 square inches. To find the new dimensions, we look for a pair of factors of 96 that also gives reasonable new dimensions of the photo. In this case, we would take the square root of the scale factor since the area is proportional to the square of the dimensions. Since we want the area to be half (scale factor of 0.5), we take the square root of 0.5, which is approximately 0.7071. Multiplying the original dimensions by this number gives us the new dimensions:
Width = 12 inches × 0.7071 ≈ 8.5 inches
Length = 16 inches × 0.7071 ≈ 11.3 inches
All calculations are approximate, assuming that Tina trims the photo uniformly. Therefore, the smaller photo should have dimensions of approximately 8.5 inches by 11.3 inches.