Rhombus and diagonals

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

Correct answer:

h =  12 cm

Step-by-step explanation:

S=150 cm2 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 cm u1​=3k=3⋅ 5=15 cm u2​=4k=4⋅ 5=20 cm a2 = (u1​/2)2+(u2​/2)2  a=(u1​/2)2+(u2​/2)2​=(15/2)2+(20/2)2​=225​=12.5 cm   S = ah h=S/a=150/12.5=12 cm

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