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

Sagot :

Lanuel

Answer:

Dimensions = 4cm, 11cm and 21cm

  OR

Dimensions = 4cm, -21cm and -11cm

Step-by-step explanation:

Solving the quadratic equation by using the factorization method;

x² + 12x - 220 = 0

Factors = 22 and -10

x² + 22x - 10x - 220 = 0

x(x + 22) - 10(x + 220) = 0

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

Therefore, x = 10 or x = -22

Given the following data;

Length of one side = (x + 1)cm

When x = 10

Length of one side = (10 + 1)cm

Length of one side = 11cm.

When x = -22

Length of one side = (-22 + 1)cm

Length of one side = -21cm

Length of the other side = (x + 11)cm

When x = 10

Length of the other side = (10 + 11)cm

Length of the other side = 21cm

When x = -22

Length of the other side = (-22 + 11)cm

Length of the other side = -11cm

Check;

Volume of a cuboid = L*L*L

Volume of a cuboid = 4 * 11 * 21

Volume of a cuboid = 924cm³

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