1. The volume of a cuboid iscalculated by multiplying itslength, width, and height. In thiscase, the volume is given as924 cm³.
2. The dimensions of the cuboidare given as 4 cm, (x + 1) cm, and(x + 11) * cm .
3. Using the formula for volume,we can set upthe followingequation: 4^ * (x+1)^ * (x + 11) = 924
4. Simplifying the equation, wehave (x+1)^ * (x + 11) = 924/4
5. Multiplying the factors, we getx ^ 2 + 12x + 11x + 11 = 231
6. Combining like terms, we have v² + 22v + 11 = 231
7. Rearranging the equation, we get x² + 23x-220 = 0.
Now, let's solve the equation by factorization:
8. To factorize the quadratic equation x² + 23x - 220 = 0, we need to find two numbers that multiply to give -220 and add up to 23.
9. After finding the correct factors, we can rewrite the equation as (x - a) * (x - b) = 0, where a and b are the values that satisfy the conditions.
10. In this case, the factors are -20 and 11. So the factorized,
equation is (x-11)^ * (x + 20) = 0
11. Setting each factor equal to zero, we have two possible values for x / x - 11 = 0 , and x + 20= 0.
12. Solving these equations, we find x = 11 and x = - 20 .
Finally, let's find the dimensions of the cuboid:
13. Using the values of x, we substitute them into thedimensions given:
- For x = 11 the dimensions are4 cm,12 cm, and 22 cm.
- For x = - 20 : the dimensionsare 4 cm, -19 cm, and -9 cm.