1. A rectangular box has a volume of (2x³ + 3x² − 8x+ 3)cm³. If the length of
the box is (x+ 3)cm and the width is (x− 1)cm, find the height in terms of x.
the box is (x+ 3)cm and the width is (x− 1)cm, find the height in terms of x.
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Answer:
H = 2x - 1 cm
Step-by-step explanation:
Volume of a rectangle
The volume of a rectangle can be calculated by the formula:
V = l x w x h
where V is the volume, l is the length, w is the width and h is the height.
The given are the volume of a rectangular box of (2x³ + 3x² − 8x+ 3)cm³, length of (x+3)cm and width of (x -1 )cm. We need to find the height in terms of x.
Step 1: Rearrange the formula in terms of height and substitute the given values in terms of x in the resulting formula and simplify.
h =
h =
h =
Step 2: Notice that we have a polynomial in the numerator and a trinomial in the denominator that can be factored out.
h =
h =
Step 3: Cancel out like terms in the numerator and the denominator. Hence,
h = 2x - 1 cm
Therefore, the height is 2x -1 cm.
To learn more about polynomial and trinomial factoring, click on the link below:
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