Answer:
[tex]0< b\leq 14.5[/tex]
Step-by-step explanation:
Let's set up our equation. We know that rectangles have two pairs of equal sides. We are also given that one pair of those sides is 1 unit longer than the other pair. Finally, we are told that the perimeter is at most 60 meters. 'At most' tells me to set up an inequality.
I'm going to set up two equations to solve this problem. First, let [tex]a[/tex] be the longer side and [tex]b[/tex] be the shorter side.
[tex]2a+2b\leq 60[/tex]
Next, because the sides are consecutive integers and [tex]b[/tex] is shorter, we can say that [tex]a-b=1[/tex].
We now have a system of equations. I will solve using substitution.
[tex]a-b=1\\a=b+1[/tex]
Substitute [tex]a[/tex] into the first equation.
[tex]2(b+1)+2b\leq 60[/tex]
Solve algebraically.
[tex]2b+2+2b\leq 60\\4b+2\leq 60\\4b\leq 58\\b\leq 14.5[/tex]
So, [tex]b[/tex] could be any integer between 0 (since distance cannot be negative) and 14.5, also written as [tex]0<b\leq 14.5[/tex].
I hope this helped!
