Given a rhombus with diagonals 6 and 8. Find the height of the rhombus.

univerkov | May 29, 2021 | education

1. Vertices of the rhombus – A, B, C, D. AC = 8 units. ВD = 6 units. ВН – height. О is the point of intersection of the diagonals. С is the area of the rhombus.

2. Triangle AOD is rectangular, since the diagonals of the rhombus are perpendicular.

AO = 1/2 AC = 8: 2 = 4 units.

DO = 1/2 BD = 6: 2 = 3 units.

AD = √AO² + DO² = √4² + 3² = √16 + 9 = 5 units.

3. S = АС х ВD / 2 = 8 х 6/2 = 24 units of measurement².

4. S = АD х ВН = 24 units of measure².

ВН = 24: 5 = 4.8 units.

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