Find the length of the longest side of the rectangle whose vertices are given. a(2, 1), b(5, 4), c(0, 3), d(3, 6)

Draw an accurate picture of the rectangle in the x-y axis, as shown in the figure.

Clearly the longest sides are Ab and CD.

Draw point E, such that AE is perpendicular to BE.

E has the x-coordinate equal to that of B, and the y coordinate equal to that of A.

So the coordinates of E are (5, 1)

Since AE and EB are perpendicular, m(AEB)=90°.

|AE|=|EB|=3, so by the pythagorean theorem:

units

  units