Final answer:
The total length of the wire used to fence the rectangular piece of land is 97 meters.
Step-by-step explanation:
To find the total length of the wire used to fence the rectangular piece of land, we need to find the perimeter of the rectangle.
The perimeter is calculated by adding the lengths of all the sides of the rectangle.
Since the rectangle has two sides measuring 15m and two sides measuring 31m, we can calculate the total length of wire used as follows:
Length of wire = 2(15m) + 2(31m) + 5m (for the gate)
= 30m + 62m + 5m
= 97m
So, the total length of the wire used to fence the rectangular piece of land is 97 meters.