Inside a triangle formed by the line 3x+4y=1 and the positive coordinate axis, inscribe a square with three of the vertices on the coordinate axes and one vertex on the line.

Question

1) Find the length of a side of the square.
In the triangular region described above inscribe a rectangle that has one vertex in the origin of the coordinate system and another vertex - on the line. Find the dimensions of this rectangle, if it is twice as wide as it is tall.

Answer 1

you want the width equal to the height. So, y=x and

x = (1-3x)/4
4x = 1-3x
x = 1/7

For the rectangle, you want x = 2y
so solve a similar equation.