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A cuboid with a volume of 924cm^3 has dimensions 4cm, (x+1)cm and (x+11). Show clearly that x^2+12x-220=0 solve the equation by factorisation, making sure you show the factorisation. Finally, find the dimensions of the cuboid,

Sagot :

MrRoyal

Answer:

[tex]x^2+12x-220=0[/tex] -- Proved

[tex]x = 10\ \ \ x = -22[/tex]

Step-by-step explanation:

Given

[tex]Volume = 924cm^3[/tex]

[tex]Dimension: 4cm; (x+1)cm; (x+11)cm[/tex]

Required

Show that [tex]x^2+12x-220=0[/tex]

The volume is calculated as:

[tex]4 * (x + 1) * (x + 11) = 924[/tex]

Open the brackets

[tex](4x + 4) * (x + 11) = 924[/tex]

[tex]4x^2 + 44x + 4x + 44 = 924[/tex]

[tex]4x^2 + 48x+ 44 = 924[/tex]

Collect Like Terms

[tex]4x^2 + 48x+ 44 - 924=0[/tex]

[tex]4x^2 + 48x -880=0[/tex]

Divide through by 4

[tex]\frac{4x^2}{4} + \frac{48x}{4} -\frac{880}{4}=0[/tex]

[tex]x^2+12x-220=0[/tex]

Solving further:

Expand the expression

[tex]x^2 + 22x - 10x - 220 = 0[/tex]

Factorize:

[tex]x(x + 22) - 10(x + 22) = 0[/tex]

[tex](x - 10)(x + 22) = 0[/tex]

Split:

[tex]x - 10 = 0;\ \ \ x + 22 = 0[/tex]

[tex]x = 10\ \ \ x = -22[/tex]

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