The area of the rhombus is 367.5 dm2. Find the diagonals of the rhombus if they are 3: 5.

In order to find the lengths of the diagonals of a rhombus, we will compose and solve an equation using the formula for finding the area of a rhombus through the diagonals.

The condition says that the area of the rhombus is 367.5 dm2. It is also known that the diagonals relate to each other as 3: 5.

We introduce the variable k – the coefficient of similarity, then the lengths of the diagonals: 3k and 5k.

To find the formula for finding the area, we will use.

S = 1/2 * d1 * d2.

1/2 * 3k * 5k = 367.5;

7.5k ^ 2 = 367.5;

k ^ 2 = 367.5: 7.5;

k = 7.

3 * 7 = 21 dm is the length of one diagonal of the rhombus, then 5 * 7 = 35 dm is the length of the second diagonal of the rhombus.