Question 165454
the largest area enclosed by a rectangle is actually a square
__ a square with a perimeter of 20ft has four 5ft sides
__ so the area is 25sqft



to get technical __ the perimeter is 20ft, so L+W=10 (half the perimeter) __ L=10-W


the area is L times W __ A=L*W __ substituting A=(10-W)*W __ A=10W-W^2


A=-W^2+10W is a downward opening parabola __ the maximum value for A occurs at the axis of symmetry


the equation for the axis of symmetry is W=-(10)/(2*(-1)) __ W=5


substituting __ L+(5)=10 __ L=5


A=L*W __ A=5*5 __ A=25