Sides of rectangle ABCD: AB = 6 BC = 8 Find the length of the vector DA and AC?

1. Since ABCD is a rectangle, then AB = CD = 6 and DA = BC = 8, hence the length of the vector DA is 8.

2. The AC diagonal divides the rectangle into two right-angled triangles and is the hypotenuse in them. The legs are the sides of the rectangle. By the Pythagorean theorem:

AB ^ 2 + BC ^ 2 = AC ^ 2.

Let’s find the AC:

AC = √ (AB ^ 2 + BC ^ 2) = √ (6 ^ 2 + 8 ^ 2) = √ (36 + 64) = √100 = 10.