If Jack cuts the rectangular sheet of paper in half, he will get two identical rectangles that are similar to the original sheet of paper. This means that the ratio of the sides of the original rectangle is the same as the ratio of the sides of each of the new rectangles.
Let's say that the longer side of the original rectangle is x cm long. Then, the shorter side is 27 cm long. When Jack cuts the rectangle in half, each of the new rectangles will have a shorter side of 27 cm and a longer side of x/2 cm.
Since the new rectangles are similar to the original rectangle, we know that the ratio of the longer side of the original rectangle to the shorter side of the original rectangle is the same as the ratio of the longer side of the new rectangle to the shorter side of the new rectangle. This can be written as:
x/27 = (x/2)/27
We can solve this equation for x:
x/27 = x/54
54x = 27x
27x = 0
x = 0
This answer doesn't make sense because the length of the longer side of the original rectangle can't be 0. The reason we got this answer is that we made a mistake in the equation. We should have written:
x/27 = 27/(x/2)
This equation can be simplified to:
x^2 = 27*54
x^2 = 1458
x = sqrt(1458)
x = 38.15 cm (rounded to 3 s.f.)
Therefore, the longer side length of the original sheet of paper is 38.15 cm (rounded to 3 s.f.).