Final answer:
The ratio of the longer side to the shorter side is 1:1.
Step-by-step explanation:
To find the ratio of the longer side to the shorter side, we need to determine the dimensions of the rectangle. Let's assume the shorter side has a length of 'x' inches. Since the crease formed is the same length as the longer side, the longer side also has a length of 'x' inches. When the diagonally opposite corners are brought together, it forms a right triangle with the crease as the hypotenuse. Using the Pythagorean theorem, we can find the length of the crease. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, one of the sides is 'x' and the other side is 'x/2' (half of the shorter side). So, we have x^2 = x^2/4 + x^2/4. Simplifying this equation, we get 4x^2 = x^2 + x^2/4. Combining like terms, we have 4x^2 = 5x^2/4. Multiplying both sides of the equation by 4/5, we get 16x^2/5 = x^2. Dividing both sides by x^2, we get 16/5 = 1. Dividing both sides by 1, we get 16/5 = x^2. Taking the square root of both sides, we get x = sqrt(16/5). Simplifying this expression, we get x = (2 * sqrt(5))/sqrt(5). The square root of 5 in the numerator and denominator cancel out, so we are left with x = 2. Therefore, the shorter side of the rectangle is 2 inches and the longer side is also 2 inches. The ratio of the longer side to the shorter side is 2:2, which simplifies to 1:1.