Answer:
- x² +12x -220 = 0
- (x -10)(x +22) = 0
- x = 10, -22
- dimensions: 4 cm, 11 cm, 21 cm
Explanation:
The volume of a cuboid is given by the product of its dimensions. That fact can be used to find unknown values related to the dimensions.
V = LWH
a)
924 cm³ = (4 cm)((x +1) cm)((x +11) cm) . . . . use the given values
231 = (x +1)(x +11) . . . . . . divide by 4 cm³ to simplify a bit
x² +12x +11 = 231 . . . . . . eliminate parentheses
x² +12x -220 = 0 . . . . . . subtract 231
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b)
To factor this equation, we need factors of -220 that have a total of 12.
-220 = (-1)(220) = (-2)(110) = (-4)(55) = (-5)(44) = (-10)(22) = (-11)(20)
Sums of these factor pairs are 219, 108, 51, 39, 12, 9. The pair we want is (-10)(22). This tells us the factored form of the equation is ...
(x -10)(x +22) = 0
The values of x that make these factors zero are the solutions to the equation:
x = 10, x = -22
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c)
The negative value of x will give negative values for the dimensions, so we're only interested in the positive solution to the equation: x = 10. The unknown dimensions are (x +1) and (x +11), so the cuboid's dimensions are ...
4 cm, 11 cm, 21 cm
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Check
The volume of the cuboid with those dimensions is ...
(4 cm)(11 cm)(21 cm) = 924 cm³ . . . . answer checks OK