How would you find the dimensions of a rectangle when one side is 2 cm greater than the other side and its area in square cm is equal to its perimeter in cm?

Answer 1

Suppose the smaller side is x cm.

Then the larger side is x+2 cm.

The area (in sq cm) is x*(x+2) = x2 + 2x

while the perimeter is 2*[x + (x+2)] = 2*[2x + 2] = 4x + 4

Now Area = Perimeter implies that x2 + 2x = 4x + 4

or x2 - 2x - 4 = 0

Solving this quadratic equation, using the quadratic formula, gives

x = -1.2361 or x = 3.2361.

Since x is a length of the rectangle, it cannot be negative so it must be 3.2361 cm

Then the other side of the rectangle is 5.2361 cm.

These dimensions give an area of 16.9443 cm2 and a primeter of 16.9443 cm, as required.

The exact value of x is 1 + sqrt(5)