Points A, B, and C, form a triangle . The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards . Pete walks directly from point A to point C, without passing through point B . What is the direct distance from A to C? How far would Pete walk if he went from A to B to C? square yards The direct distance from A to C is more than square yards. The inequality w wlt represents the distance, w , that Pete might save by taking the direct path.

To find the direct distance from point A to point C, we can use the triangle inequality theorem. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.<br /><br />In this case, we know that the distance between point A and point B is 15 yards, and the distance between point B and point C is 25 yards. Therefore, the sum of these two distances is 40 yards.<br /><br />According to the triangle inequality theorem, the direct distance from point A to point C must be less than the sum of the lengths of the other two sides. In other words, the direct distance from A to C is less than 40 yards.<br /><br />If Pete walks from point A to point B to point C, he would walk a total distance of 15 yards + 25 yards = 40 yards.<br /><br />Therefore, the direct distance from A to C is more than 15 yards but less than 40 yards.<br /><br />The inequality w < 40 represents the distance, w, that Pete might save by taking the direct path.