A rectangular box has a volume of (x³ + 5x² – 12x – 36) cm³, length of (x + 6) cm and width of (x + 2) cm. What is its height?Select one:a. (x + 3) cmb. (x - 3) cmc. (x + 4) cmd. (x - 4) cm
Question
A rectangular box has a volume of (x³ + 5x² – 12x – 36) cm³, length of (x + 6) cm and width of (x + 2) cm. What is its height?Select one:a. (x + 3) cmb. (x - 3) cmc. (x + 4) cmd. (x - 4) cm
Solution
The volume of a rectangular box is given by the formula:
Volume = Length * Width * Height
We know the volume, length, and width, so we can solve for the height by rearranging the formula:
Height = Volume / (Length * Width)
Substituting the given values:
Height = (x³ + 5x² – 12x – 36) cm³ / [(x + 6) cm * (x + 2) cm]
To simplify this, we need to factor the numerator (the volume). The volume expression factors to:
x³ + 5x² – 12x – 36 = (x + 6)(x + 2)(x - 3)
So, the height is:
Height = (x + 6)(x + 2)(x - 3) / [(x + 6)(x + 2)] Height = x - 3 cm
So, the correct answer is b. (x - 3) cm.
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