The diagonals of the rhombus are 16 cm and 48 cm. Find the segment SO – the distance from the top of S to the extension of the side PT.

univerkov | January 11, 2021 | education

The diagonals of the rhombus are halved at the point of their intersection and intersect at right angles.
Then KН = PH = KR / 2 = 16/2 = 8 cm, SH = TH = ST / 2 = 48/2 = 24 cm.
In a right-angled triangle PTH, according to the Pythagorean theorem, PT ^ 2 = PH ^ 2 + TH ^ 2 = 64 + 576 = 640.
8 * √10 cm.
Determine the area of the rhombus.
S = ST * KP / 2 = 48 * 16/2 = 384 cm2.
Also Savsd = TP * SO.
SO = Savsd / TP = 384/8 * √10 = 48 / √10 = 4.8 * √10 cm.
Answer: The length of the SO segment is 4.8 * √10 cm.

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