A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is 8 meters and the distance between the gopher's holes is 10 meters. How wide is the yard?

6 meters

Step-by-step explanation:

Since the gaps are at opposite corners, this distance corresponds to the diagonal.

If we cross the diagonal a rectangular triangle is formed and in this way we can apply Pythagoras.

d ^ 2 = l ^ 2 + w ^ 2

d = 10

l = 8

if we solve for w, that is, the width:

w ^ 2 = d ^ 2 - l ^ 2

we replace:

w ^ 2 = 10 ^ 2 - 8 ^ 2

w ^ 2 = 36

w = 6

which means that the width is 6 meters