Find the length of the longest line segment that can be drawn on a rectangular board 3.07 m by 2.24 m

You can use the Pythagorean Theorem for this because the longest segment would be drawn from one corner to the other. 

Pythagorean Theorem: a^2+b^2=c^2
a=3.07 and b=2.24 because they are the legs of the triangle
3.07^2+2.24^2=c^2 
9.4249+5.0176=c^2 (combine like terms)
14.4425=c^2 (square root both sides)
c=3.80 m 

Hope this helps!