B= Base
H=Height
2B+2H=62 -Perimeter equation
B*H=234 -Area equation
B=234/H
Plug that into your first equation
2(234/H)+2H=62
468/H+2H=62
Multiply both sides by H
468+2H^2=62H
2H^2-62H+468=0
H^2-31H+234=0
That was just some simplifying
Now we have a quadratic we have to solve for
You can use the quadratic formula
31+-√31^2-4(234)
(31+5)/2 and (31-5)/2
H=18, 13
Plug those into your B*H=234 equation
18B=234
B=13
13B=234
B=13
So the base can be 13 or 18 feet
And the height can be 13 or 18 feet
