The diagonals of the rhombus are 14 dm and 48 dm. Find the height of the rhombus.
| May 18, 2021 | education
At the rhombus, the diagonals, at the intersection point, are divided in half, then BO = BD / = 14/2 = 7 cm, CO = AC / 2 = 48/2 = 24 cm.
From the right-angled triangle BOC, by the Pythagorean theorem, we determine the hypotenuse BC.
BC ^ 2 = BO ^ 2 + CO ^ 2 = 7 ^ 2 + 24 ^ 2 = 49 + 576 = 625.
BC = 25 cm.
The sides of the rhombus are 25 cm.
Let’s define the area of a rhombus through its diagonals.
Savsd = АС * ВD / 2 = 48 * 14/2 = 336 cm2.
The area of the rhombus is also equal to:
Savsd = СD * BН.
336 = 25 * BH.
BH = 336/25 = 13.44 cm.
Answer: The height of the rhombus is 13.44 cm.
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