Rhombus and diagonals

The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.

Correct result:

h =  12 cm

Solution:

S=150 u1:u2=3:4 S=u1 u2/2 u1=3k u2=4k S=3k⋅ 4k/2 S=6 k2 k=S/6=150/6=5 u1=3k=3⋅ 5=15 u2=4k=4⋅ 5=20 a2=(u1/2)2+(u2/2)2=(15/2)2+(20/2)2=6254=156.25 a=(u1/2)2+(u2/2)2=(15/2)2+(20/2)2=252=12.5 S=ah h=S/a=150/12.5=12 cm

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