What is the length of a rectangle whose diagonal is 32 inch?

Answer 1

The diagonal of a rectangle does not provide enough information to determine the length of the rectangle.

Let L be any real number such that 32/sqrt(2) < L < 32.

let B = sqrt(32^2 - L^2)

Since L < 32 the above square root exists, and since L > 32/sqrt(2), B < L.

So the rectangle with sides of L and B will have a diagonal of 32 inches.

But L is any of an infinite number of possible real numbers. Therefore there are infinitely many possible solutions.