The height AH of the rhombus ABCD divides the side AD into segments DH is 12 and CH is 3. Find the height of the rhombus?
| September 18, 2021 | education
Determine the length of the side CD of the rhombus.
CD = CH + DH = 3 + 12 = 15 cm.
Since the quadrangle ABCD is a rhombus, then AD = CD = 15 cm.
Since AH is the height of a rhombus, the triangle ADH is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg AH.
AH ^ 2 = AD ^ 2 – DH ^ 2 = 15 ^ 2 – 12 ^ 2 = 225 – 144 = 81.
AH = 9 cm.
Answer: The height of the rhombus is 9 cm.
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