Open Middle®
Directions: Using the digits 1 – 9, at most once each, fill in the blanks to make it so that the value for the area of the rectangle (in square units) is greater that the value for the perimeter (in linear units). What is the greatest difference you can find between the area and perimeter? What is the least difference you can find?
Hint
The way to find the area of a quadrilateral is b(base) * h(height).
Answer
One answer is a base of 6 and a height of 5, and an area of 30, and a perimeter of 22.
Source: Owen Kaplinsky
When only considering rectangles where the value of the area is greater than the value of the perimenter, the greatest difference is 38 (base= 9 height= 8). The least difference is 1 (base= 3 height =7).