Question

a cuboid with a volume of 924 cm3 has dimensions 4cm (x+1)cm and (x+11)cm. show clearly that x^2 +12x-220=0. show the equation by factorisation. State both values of x. and finally find the dimensions of the cubiod.

Answer 1

Answer:

4cm, 11cm, 21cm

Step-by-step explanation:

4(x + 1)(x + 11)

4(x ^ 2 + 12x + 44)

x ^ 2 + 12x + 11 = 231

x ^ 2 + 12x + 11 - 231 = 0

x ^ 2 + 12x - 220 = 0

(x - 10)(x + 22) = 0

x = 10 and x = - 22

4cm , 11cm , 21cm

Answer 2

Both values of x are 10 and -22

The dimension of the cuboid is 4cm by 11cm by 21cm

The formula for calculating the volume of a cuboid is expressed as:

Volume of a cuboid = Length * Width * Height

Given the following parameters

Length = 4 cm

Width = (x+1) cm

Height = (x+11) cm

Volume = 924cm³

Substitute into the formula as shown:

924 = 4(x+1)(x+11)

Factorize

924 = 4(x²+11x + x + 11)

924/4 = x²+12x+11

231 = x²+12x+11

Swap

x²+12x+11 = 231

x²+12x = 231 - 11

x²+12x = 220

x²+12x - 220 = 0 (Proved)

On factorizing

x²+12x - 220 = 0

x²+22x-10x - 220 = 0

x(x+22)-10(x+22) = 0

(x-10)(x+22) = 0

x = 10 and -22

Hence both values of x are 10 and -22

Get the dimensions

Length = 4cm

Width = x+ 1 = 10 + 1 = 11cm

Height = x+11 = 10 + 11 = 21cm

Hence the dimension of the cuboid is 4cm by 11cm by 21cm

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