The distance from the intersection of the diagonals of the rectangle to the line containing its larger side is 2.5 cm. Find the smaller side.
For a rectangle, the diagonals are equal and are halved at the point of their intersection.
Then BO = DO.
The distance from point O to the AD side is the perpendicular OH to the AD side.
The segments AB and OH are perpendicular to AD, therefore the segments AB and OH are parallel.
Then OH is the middle line of the triangle ABD, which means AB = 2 * OH = 2 * 2.5 = 5 cm.
Answer: The length of the shorter side is 5 cm.
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