MY momework

The area of the rectangle in the middle is given by $5x$ where $x$ is an unknown number. Let's suppose $x$ is an integer.

Then the area of the figure is given by $A=5x+(4+x)6=11x+24$ Then since the only options for $A$ are integers, $A-24$ is divisible by $11$ . The only option for $A$ is then $A=156$ .

Not sure what the question was but assume from the choices, we need area.

Let x = width of RH triangle from top to bottom.

Then distance from cutout rectangle to the other is x - 4.

Area of brown rectangle in middle is 5 * (x -4).

Height of triangle is 17/2 - 5/2 = 6.

Area of 2 triangles = 1/2 * x * 6 * 2 = 6*x

Total area = 5x - 20 + 6x

Therefore Total Area + 20 = 11x =====> (Total Area + 20)/11 = x

Only choice which gives an integer for x is 156 and x = 16