The side of the rhombus is 25 cm, the height is 24. Find the diagonals of the rhombus.

| September 12, 2021 | education

Since ВН is the height to the CD side, the ВНС and ВНD triangles are rectangular.

Consider a triangle ВНD in which, according to the condition, ВС = 25 cm as a side of a rhombus, ВН = 24 cm as a height.

Then, by the Pythagorean theorem, the leg CH ^ 2 = BC ^ 2 – BP ^ 2 = 625 – 576 = 49.

CH = 7 cm.

Then DH = DC – CH = 25 – 7 = 18 cm.

Consider the triangle ВНD and find, by the Pythagorean theorem, the hypotenuse ВD, which is one of the diagonals of the rhombus.

BD ^ 2 = BH ^ 2 + DH ^ 2 = 24 ^ 2 + 18 ^ 2 = 576 + 324 = 900.

ВD = 30 cm.

Consider a right-angled triangle BOS, in which BC = 25 cm, BO = BD / 2 = 15 cm.

Then, by the Pythagorean theorem, OС ^ 2 = BC ^ 2 – ВO ^ 2 = 25 ^ 2 – 15 ^ 2 = 625 – 225 = 400.

OС = 29 cm.

Then the diagonal AC = 2 * OC = 40 cm.

Answer: The diagonals of the rhombus are 30 cm and 40 cm.



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