Question

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​

Answer 1

The length of the diagonals are 6mm and 18mm

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