Could a rectangle have a perimeter 20cm and area 20cm2?

Answer 1

Yes. The maximum area for a rectangle with a given perimeter is the square (in this case, 5 cm x 5 cm = 25 cm2), and any area between that and 0 is possible by slowly stretching out the square, increasing its length while decreasing its width.

If you'd like to figure out the dimensions of the rectangle with a perimeter of 20 and an area of 20 (I'll leave off the units for simplicity), we can use algebra:

Let x and y be the length and width. We know two things:

Area: xy = 20

Perimeter: 2x + 2y = 20

Solve the second equation for y and we get

y = 10 - x.

Substituting that in the first equation we get

x(10 - x) = 20

which turns into the quadratic equation

x2 - 10x + 20 = 0

Applying the quadratic equation, we get

x = 5 +/- sqrt(5), which gives us our two dimensions:

5 + sqrt(5) and 5 - sqrt(5)

Answer 2

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