# math

At the ruins of Caesarea, archaeologists discovered a huge hydraulic concrete block with a volume of 945 cubic meters. The block's dimensions are x meters high by 12x - 15 meters long by 12x - 21 meters wide. What is the height of the block?

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1. remember , volume = lwh

x(12x-15)(12x-21) = 945
simplifying a bit

x(3)(4x - 5)(3)(4x-7) = 945
x(4x-5)(4x-7) = 105
16x^3 -48x^2 +35x - 105=0
by grouping ...
16x^2(x - 3) + 35(x-3) = 0
(x-3)(16x^2 + 35) = 0
x = 3 or x^2 = -35/16 , which is not real

so the only real solution is x = 3

so the block is 3 m high,

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2. How do you get 105?

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3. I divided both sides by 9
945÷9=105
notice the (3)(3) is gone on the left side

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