The diagonals of the rhombus ABCD are 12 and 16. Find the length of the vector AB.

In order to find the length of the vector AB we will apply the following transformations.

We know from the condition that the diagonals of the rhombus ABCD are 12 and 16.

Let’s denote by O the point of intersection of the diagonals and consider one of the resulting right-angled triangles AOB.

Angle AOB = 90 °.

The point of intersection divides the diagonals into equal parts, that is, AO = AC / 2 = 12/2 = 6; BO = BD / 2 = 16/2 = 8.

To find the hypotenuse AB of the triangle AOB, we apply the Pythagorean theorem.

c = √ (a ^ 2 + b ^ 2) = √ (6 ^ 2 + 8 ^ 2) = √ (36 + 64) = √100 = 10.