Question

Is it possible for a rectangle with a perimeter of 44cm to have the area of 125cm^2 ? If so, find the dimensions of the rectangle.

Figure out the equation in general form.

Answer 1

It is not possible.
The largest area is when the perimeter of 44 describes a square, namely of 11" per side, which gives an area of 11²=121 < 125.

I assume you are in grade 11, so cannot use calculus to explain. But generally, the rectangle with the largest area for the same perimeter is a square.

If it were possible, then we have the equations:
b*h=A
2(b+h)=P
where b,h represent the dimensions of the rectangle, and A and P represent area and perimeters.
You can then solve for b and h given A and P.