The perimeter of the rectangle is 52, the difference between the distances from the point of intersection

The perimeter of the rectangle is 52, the difference between the distances from the point of intersection of the diagonals to its sides is 7. Find the smaller side of the rectangle

Segments OK and OH are perpendicular to CD and AD, and then OK is parallel to BC, OH is parallel to CD.

The diagonals AC and BD at point O are divided in half, then the segments OK and OH are the middle lines of the triangles BCD and ABD, then OK = BC / 2, OH = CD / 2.

Then Rokdn = Ravsd / 2 = 52/2 = 26 cm.

By condition, OK – OH = 7 cm.

Let OH = X cm, then OK = X + 7 cm.

Rockdn = 2 * (X + X + 7) = 26.

4 * X = 26 – 14 = 12.

X = 12/4 = 3. OH = 3 cm, then CD = 2 * OH = 2 * 3 = 6 cm.

Answer: The length of the shorter side is 6 cm.