Question

A piece of paper in the shape of ABC

has edges of lengths 6 cm, 8 cm, and
10 cm. It is folded so that point A lies
on top of point B. Find the length of
the crease.

Answer 1

To find the length of the crease, we can use the Pythagorean theorem. Since the paper is folded so that point A lies on top of point B, the crease connects point C to the midpoint of the line segment AB. Let's call this midpoint M.

Step-by-step explanation:

To find the length of the crease, we can use the Pythagorean theorem. Since the paper is folded so that point A lies on top of point B, the crease connects point C to the midpoint of the line segment AB. Let's call this midpoint M.

First, let's find the length of AM. We can use the formula for the midpoint of a line segment, which is (x1 + x2)/2 and (y1 + y2)/2. In this case, the coordinates of A are (0, 0) and the coordinates of B are (6, 8). Plugging these into the formula, we get ((0 + 6)/2, (0 + 8)/2) = (3, 4).

Next, we use the Pythagorean theorem to find the length of AM. The length of AM is sqrt((3-0)^2 + (4-0)^2)

= sqrt(9 + 16)

= sqrt(25)

= 5 cm.