The area of the rhombus is 24 cm, and one of the diagonals is 3 times larger than the other

| September 10, 2021 | education

The area of the rhombus is 24 cm, and one of the diagonals is 3 times larger than the other, find the diagonal of the rhombus.

It is known from the condition that the area of the rhombus is 24 cm, and it is also known that one of its diagonals is 3 times larger than the other. In order to find the lengths of the diagonals of a rhombus, we will apply the formula to calculate the area of a rhombus in terms of the lengths of the diagonals.

Let’s remember the formula:

S = 1/2 * d1 * d2.

We denote by x cm the length of one of the diagonal, then the length of the second diagonal is written as 3x cm.

We write down the equation and solve it:

1/2 * x * 3x = 24;

1.5x ^ 2 = 24;

x ^ 2 = 36;

x = 6 cm the length of the smaller diagonal and 6 * 3 = 18 cm the length of the larger diagonal.



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