Question

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)

Answer 1

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:

$|AB|= \sqrt{ |AE|^{2} + |EB|^{2} }= \sqrt{3^{2}+ 3^{2}} = \sqrt{2*3^{2}}=3 \sqrt{2}$ units


Answer: $3\sqrt{2}$ units