The diagonals of the rhombus ABCD are 12 and 16. Find the length of the vector AD-AC.

In the condition, we are not given a drawing, but it will not be difficult to find it on the Internet or draw it ourselves.

We know from the condition that the given quadrangle is a rhombus.

It is known that its diagonals are 12 and 16.

Let’s take a look at a diamond. Let BD = 12, AC = 16.

The point of intersection of the diagonals – point O divides the diagonals of the rhombus into two equal parts. We write down the equalities BO = DO = 6, AO = CO = 8.

we conclude that the length of the vector AD and AC is equal to DC.

Consider a right-angled triangle ODC:

It has OC = 8; OD = 6; Angle O = 90 °.

Let’s apply the Pythagorean theorem to calculate the hypotenuse of a triangle. Let’s write equality for a triangle:

CD ^ 2 = OC ^ 2 + OD ^ 2;

CD ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100

CD = 10.