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Question
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
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Solution
Volume of cuboid = (length) × (width) × (height)
We have, 12ky2 + 8ky – 20k
= 4[3ky2 + 2ky – 5k]
= 4[k(3y2 + 2y – 5)]
= 4 × k × (3y2 + 2y – 5)
= 4k[3y2 – 3y + 5y – 5]
= 4k[3y(y – 1) + 5(y – 1)]
= 4k[(3y + 5) × (y – 1)]
= 4k × (3y + 5) × (y – 1)
Thus, the possible dimensions of the cuboid are 4k, (3y + 5) and (y – 1).
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