Answer:
12.9 m
Explanation:
Let d represent the length of the diagonal. Then d-2 is the length and d-6 is the width. The Pythagorean theorem can be used to relate these measures, which are the legs and hypotenuse of a right triangle.
d² = (d-2)² + (d-6)²
d² = d² -4d +4 + d² -12d +36 . . . . eliminate parentheses
0 = d² -16d +40 . . . . . . . . . . . . . . . subtract d², collect terms
0 = d² -16d +64 -24 . . . . . . . . . . . rearrange the constant to make a square
0 = (d -8)² -24 . . . . . . write in vertex form
d -8 = √24 . . . . . . . . . add 24 and take the square root
d = 8 + √24 . . . . . . . . the negative square root is extraneous in this problem
d ≈ 12.9 . . . meters
The length of the diagonal is about 12.9 meters.