one diagonal of a rhombus is tree times long as the other diagonal if the area of the rhombus is 54 square millimeters what is the length of the diagonals

The length of the diagonals are 6mm and 18mm

Step-by-step explanation:

In this question, we are tasked with calculating the lengths of the diagonals of a rhombus, given the area of the rhombus and how the two diagonals differ from each other.

Mathematically, for a rhombus, we can calculate the area of the rhombus using the formula.

A = 1/2 * d1 * d2

We are also told in the question that one diagonal is there times longer than the other.

So we can say that d1 = 3d2

hence our A becomes;

A = 1/2 * 3d2 * d2

For clarity sake, let's call d2 d only

Hence

54 = 1/2 * 3d * d

3d^2 = 108

d^2 = 108/3

d^2 = 36

d = square root of 36

d = + 6 or - 6

we ignore - 6 as lengthy cannot be negative

hence d = d2 = 6mm

But d1 = 3d2

d1 = 3 * 6 = 18mm