We write the area using the width and length expression using width.
A = w(10 - w).
A = 10w - w2 .
The relationship of the area is quadratic. It has a max value that is where the vertex of the parabola is. The vertex is the average of the two zeros of the equation. We have
w1 = 0
and
w2 = 10.
1/2 (0 + 10) = 5 feet.
Martha will have largest area garden if (l = w = 5 feet).