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WITCHER [35]
3 years ago
6

The volume of a square prism is 144x^3 +216x^2 +81x

Mathematics
1 answer:
Svetach [21]3 years ago
6 0

Answer:

Equation for the perimeter of prism's square face: 16x + 12

Step-by-step explanation:

Volume of Square prism = Length * Width * Height

                                         = 144 x^3 + 216 x^2 +81 x

taking 9x common = 9x( 16 x^2 + 24 x + 9)

                               = 9x ( (4x)^2 + 2(4x)(3) + (3)^2 )

                                = 9x ( 4x+3)^2

so the length is 9x, width is 4x+3 and height is 4x+3

Now, Perimeter of prism's square face = 2* Width + 2 * Height

                                                                = 2* (4x+3) + 2* (4x+3)

                                                                = 8x +6 + 8x + 6

                                                                = 16x +12

                   

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2x +y = 20~~....(i)\\\\6x -5y = -4~~....(ii)\\\\\\\text{Multiply equation (i) by 3:}\\\\6x +3y = 60~~...(iii)\\\\(iii)-(ii):\\\\6x+3y - 6x+5y = 60-(-4)\\\\\implies 8y = 60+4 = 64\\\\\implies y = \dfrac{64}8\\\\\implies y = 8\\\\\\\text{Substitute y =8 in equation (i):}\\\\2x+8 =20\\\\\implies 2x = 20-8 = 12\\\\\implies x = \dfrac{12}2 = 6\\\\\text{Hence (x,y) = (6, 8)}

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