The values of x are -22 and 10
The dimensions are 4 cm , 11 cm , 21 cm
Step-by-step explanation:
The given is:
- A cuboid with a volume of 924 cm³
- It has dimensions 4 cm , (x + 1) cm and (x + 11) cm
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
#LearnwithBrainly
