Question

What can be the possible length of AC on segment ABCD, if AB is 2cm, BC is 4cm and CD is 3cm​

Answer 1

To determine the possible length of AC on segment ABCD, 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.

In the given quadrilateral ABCD, if AC is a segment within the quadrilateral, then we can consider triangles ABC, BCD, and ACD.

Let's examine each triangle:

1. Triangle ABC: - AB = 2 cm - BC = 4 cm - AC = ? (the length we want to find)

2. Triangle BCD: - BC = 4 cm - CD = 3 cm - BD (the diagonal of the quadrilateral) = BC + CD = 4 cm + 3 cm = 7 cm

3. Triangle ACD: - AC = ? (the length we want to find) - CD = 3 cm - AD (the diagonal of the quadrilateral) = AB + BC + CD = 2 cm + 4 cm + 3 cm = 9 cm

Now, let's apply the triangle inequality theorem to each triangle:

1. For triangle ABC: - AC + BC > AB - AC + 4 cm > 2 cm - AC > 2 cm - 4 cm - AC > -2 cm (This doesn't make sense in the context of lengths, so we ignore it.)

2. For triangle BCD: - BC + CD > BD - 4 cm + 3 cm > 7 cm - 7 cm > 7 cm (This is true.)

3. For triangle ACD: - AC + CD > AD - AC + 3 cm > 9 cm - AC > 9 cm - 3 cm - AC > 6 cm

Therefore, the possible length of AC on segment ABCD is greater than 6 cm. However, we cannot determine an exact length without additional information about the angles or side lengths of the triangles involved.