sketch the triangle with vertex on the y-axis and base on the x-axis.

two 3-4-5 triangles are formed in quads I and II

using the first quadrant triangle, the line formed by side of length 5 has the equation

consider a rectangle with upper right corner on the this line

area of a rectangle in quad I ,

maximize this one, and using symmetry, double the result to get the overall max area.