Final answer:
To relate the dimensions of two rectangles with areas in a 6/5 ratio, you need to find the scale factor 'k' which is the square root of 6/5, making the side lengths of the larger rectangle 'ka' and 'kb', where 'a' and 'b' are the dimensions of the original rectangle.
Step-by-step explanation:
When comparing two rectangles with a scale factor, one rectangle's dimensions are scaled versions of the other's. Given that one rectangle's area is 6/5 of the other, the side lengths of the larger rectangle should be scaled appropriately. For instance, if the side lengths of the original rectangle are 'a' and 'b', the larger rectangle's side lengths will be 'ka' and 'kb', where 'k' is the scale factor. To find 'k', one can set up the equation relating the area of the larger rectangle to the area of the smaller one: (ka)*(kb) = (6/5)ab.
Since the area of a rectangle is simply the product of its lengths, one can deduce that k squared must equal the ratio of the areas (k^2 = 6/5), which gives us the scale factor k equal to the square root of 6/5 when solving for 'k'. To find the specific dimensions of either rectangle, more information on the original rectangle's side lengths is required. However, the relationship between the side lengths of both rectangles is governed by the same scale factor.To ensure an appropriate understanding of scale factors and dimensional relationships, let's consider a direct proportion of a rectangle's width and length. For example, if the original rectangle had dimensions 5 inches by 10 inches, a rectangle that is 6/5 the area of the original would have dimensions of 5k inches by 10k inches, where we calculate 'k' as above.