Question

What is the maximum possible area of a parallelogram with one side of length 2 meters and a perimeter of 24 meters ?

• A. $40m^2$.
• B. $22m^2$.
• C. $25m^2$.
• D. $20m^2$.

Answer 1

The correct option is D $20m^2$.

If one side of the parallelogram is 2 meters long, then the opposite side must also be 2 meters long. You can solve for the unknown sides, which are equal in length, by writing an equation for the perimeter: 24 =2(2) + 2x, with x as the unknown side.

Solving, you get $x=10$ meters.

The parallelogram with these dimensions and maximum area is a rectangle with $2metres$ and $10metres$ sides.

Thus, the maximum possible area of the figure is: (2 m)(l0 m) $=20m$ ${}^2$.