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Solving a Cuboid Volume Problem: Dimensions of a Cuboid with Given Volume

This problem involves finding the dimensions of a cuboid with volume 60 cm³, where two dimensions are expressed in terms of a variable. The cuboid has one fixed side of 5 cm, and the other two sides are x cm and x + 4 cm. By establishing an equation for the volume ( V = 5 cdot x cdot (x + 4) = 60 ), we can simplify and solve for x using the quadratic equation. The solution reveals that x = 2 cm, allowing us to determine the dimensions as 5 cm, 2 cm, and 6 cm.

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Solving a Cuboid Volume Problem: Dimensions of a Cuboid with Given Volume

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  1. GSCE Mathematics Problem Solving Algebra Higher Tier

  2. A cuboidhassides 5 cm by x cm by x + 4cm. The volume of the cuboid is 60cm3. What are the dimensions of the cuboid ? 5cm Helping hand x + 4 x Write an equation for the volume of the cuboid and solve

  3. Answer Volume of cuboid = 5 x ( x + 4) = 60 5x2 + 20x = 60 5x2 + 20x – 60 = 0 5(x2 + 4x – 12) = 0 x2 + 4x – 12 = 0 (x + 6 ) ( x – 2 ) = 0 x + 6 = 0 or x – 2 = 0 x = -6 x = 2 x can’t be -6 cm so x = 2cm The dimensions are 5cm by 2cm by 6cm

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