The values of x are -22 and 10
The dimensions are 4 cm , 11 cm , 21 cm
Step-by-step explanation:
The given is:
We want to show that x² + 12x - 220 = 0, and solve the equation to find its dimensions
The volume of a cuboid is the product of its three dimensions
∵ The dimensions of the cuboid are 4 , (x + 1) , (x + 11)
∴ Its volume = 4(x + 1)(x + 11)
- Multiply the two brackets and then multiply the product by 4
∵ (x + 1)(x + 11) = (x)(x) +(x)(11) + (1)(x) + (1)(11)
∴ (x + 1)(x + 11) = x² + 11x + x + 11 ⇒ add like terms
∴ (x + 1)(x + 11) = x² + 12x + 11
∴ Its volume = 4(x² + 12x + 11)
∴ Its volume = 4x² + 48x + 44
∵ The volume of the cuboid = 924 cm³
- Equate the expression of the volume by 924
∴ 4x² + 48x + 44 = 924
- Subtract 924 from both sides
∴ 4x² + 48x - 880 = 0
- Simplify it by dividing all terms by 4
∴ x² + 12x - 220 = 0
Now let us factorize it into two factors
∵ x² = x × x
∵ 220 = 22 × 10
∵ 22(x) - 10(x) = 12x ⇒ the middle term
∴ x² + 12x - 220 = (x + 22)(x - 10)
∴ (x + 22)(x - 10) = 0
- Equate each factor by 0 to find x
∵ x + 22 = 0 ⇒ subtract 22 from both sides
∴ x = -22
∵ x - 10 = 0 ⇒ add 10 to both sides
∴ x = 10
∴ The values of x are -22 and 10
We can not use x = -22 because there is no negative dimensions, then we will use x = 10
∵ The dimensions are 4 , (x + 1) , (x + 11)
∵ x = 10
∴ The dimensions are 4 , (10 + 1) , (10 + 11)
∴ The dimensions are 4 cm , 11 cm , 21 cm
Learn more:
You can learn more about the factorization in brainly.com/question/7932185
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Answer: Showed that: [tex]x^2+12x-220=0[/tex].
Both values of x are -22 and 10.
The dimensions are: 4 cm, Â 11 cm, Â 21 cm.
The given dimensions are 4cm,(x + 1)cm and (x + 11)cm.
So the volume is = [tex]4(x+1)(x+11)[/tex].
Given that volume= 924 [tex]cm^3[/tex].
Equating the volumes we get:
[tex]4(x+1)(x+11)=924\\4(x^2+12x+11)=924\\x^2+12x+11=\frac{924}{4}\\ x^2+12x+11=231\\x^2+12x+11-231=0\\x^2+12x-220=0\\[/tex]
Then we factor and solve the equation:
[tex]x^2+12x-220=0\\x^2+22x-10x-220=0\\x(x+22)-10(x+22)=0\\(x+22)(x-10)=0\\x=-22,10\\[/tex]
Since x can not be negative, so x = 10.
So the dimensions are: 4 cm, (x + 1) = (10 + 1) = 11 cm, (x + 11) = (10 + 11) = 21 cm.
Learn more: https://brainly.com/question/16955358
