# The area of the rhombus is 48 dm ^ 2. the height is 2 dm less than the side. find the sides of the diamond.

March 31, 2021 | education

| In order to find the sides of a rhombus, we will compose and solve equations. To do this, we will use the formula for finding the area of a rhombus through the side and the height dropped on it.

The condition says that the area of the rhombus is 48 dm2. It is also known that the height is less than the side by 2 dm.

We denote by x dm the side of the rhombus, then the height dropped on it is (x – 2) dm.

S = a * h;

Where a is the side of the rhombus and h is the height.

We get the equation:

x (x – 2) = 48;

x ^ 2 – 2x – 48 = 0;

D = (-2) ^ 2 – 4 * 1 * (-48) = 4 + 192 = 196;

x1 = (2 + 14) / 2 = 8;

x2 = (2 – 14) / 2 = -6.

The side of the rhombus is 8 in.

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