can anyone please help me step by step on how to solve this problem?
Answers
Answer:
Step-by-step explanation:
Answer:
2cm, 11 cm, 17 cm
Step-by-step explanation:
Volume of a cuboid = length × Width × height
In our case :
Volume = 2 × (x + 3) × (x + 9)
= (x² + 3x + 9x + 27)2
= 2x²+ 24x + 54
2x² + 24x + 54 = 374
Divide through by 2:
x² + 12x + 27 = 187
x² + 12x + 27 - 187 = 0
x² + 12x - 160 = 0
We solve the quadratic equation.
We need to find the roots :
The roots are : +20 and - 8
We then expand the equation as follows :
x² + 20x - 8x - 160 = 0
x(x + 20) - 8(x + 20) = 0
(x - 8)(x + 20) = 0
x - 8 = 0
x = 8
x + 20 = 0
x = - 20
The value of x is thus :
x = - 20 or 8
But since we are dealing with dimensions in centimeters we take the positive value of x given that measurement cannot be negative.
So :
x = 8 cm
The dimensions of the cuboid are :
(8 + 3) = 11 cm
(9 + 8) = 17 cm
Dimensions of the cuboid : 2cm, 11 cm, 17 cm