Bobosharif S. answered • 02/28/18

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Volume of the block is x(12x-15)(12x-21). This is from one side. From the other side we know that this volume is equal to 945.

Now we "equal both sides":

x(12x-15)(12x-21)=945 [(12x-15=3(4x-5) and 12x-21=3(4x-7) ]

9x(4x-5)(4x-7)=945 (dived both sides by 9)

x(4x-5)(4x-7)= 105

x(16x

^{2}-48x+35)-105=0x(16x

^{2}+35)+48x^{2}-105=0x(16x

^{2}+35)-3(16x^{2}+35)=0(x-3)(16x

^{2}+35)=0Since 16x

^{2}+35≠0 for x from real numbers, then x=3.So, Height: x=3

Length: 12x-15=36-15=21

Width: 12x-21= 36-21=15

Check: 3*21*15= 945