The diagonals of the rhombus are equal to 8 and 3 units. Write the equations of the sides of the rhombus if the large

| August 7, 2021 | education

The diagonals of the rhombus are equal to 8 and 3 units. Write the equations of the sides of the rhombus if the large diagonal lies on the OX axis, and the smaller one on the OY axis. Calculate the distance between the parallel sides of this diamond.

According to the properties of the diagonals of the rhombus, the origin of coordinates O is the middle of each diagonal. Parallel sides lie on lines AB and CD and on lines BC and AD, the distance between which is equal.

| OA | = | ОC | = 4 and | ОВ | = | ОD | = 1.5. The slope of the straight lines AB and CD k = ОВ / ОА = 3/8.

Equations for AB and CD: y = 3x / 8 + 1.5 and y = 3x / 8 – 1.5.

In general terms: 3x – 8y + 12 = 0 and 3x – 8y – 12 = 0.

Using the formula for the distance between parallel lines, we find:

D = | (-12 – 12) | / √ (3 * 3 + 8 * 8) = 24 / √ 73



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