As a packaging designer you are asked to create a box of a food container with the following steps:
1. Make sketch plans of 2 rectangular open boxes such that
a) The heights of the boxes are the same; and
b) The boxes can hold 240 cm3 and 270 cm3 respectively.
2. Write a quadratic equation that would represent the volume of each box.
3. Solve each quadratic equation using any method to determine the dimensions of the materials to be used in constructing each box.
Answers
Answer:
Let the dimensions of box one be ,
Length = 8 cm
Breadth = 2 cm
Height = 15 cm
Assume the breadth to be x then we can say that ,
The length of the box is greater than the breadth by 6 and the height is 15 cm .
So equation formed = ( x + 6 ) x (15)
=> 15x ( x + 6 )
=> 15x² + 90x = 240 cm³
Let the dimensions for box two be
Length = 6 cm
Breadth = 3 cm
Height = 15 cm
Assume the breadth to be x then we can say that ,
The length of the box is greater than the breadth by 3 and the height is 15 cm .
So equation formed = ( x + 3 ) x (15)
=> 15x ( x + 3 )
=> 15x² + 45x = 270 cm³
Now solving the equations ,
First equation ,
= 15x² + 90x - 240 = 0
= Divide it by 15
= x² + 6x - 16
= x² + 8x - 2x - 16
= x ( x + 8 ) - 2 ( x + 8 )
= ( x + 8 ) ( x - 2 )
So either x = 2 or - 8
But breadth can't be negative so b is 2 and length is 8
Hence verified
For second equation ,
= 15x² + 45x - 270 = 0
= Divide by 15
= x² + 3x - 18
= x ² + 6x - 3x - 18
= x ( x + 6 ) - 3 ( x + 6 )
= ( x + 6 ) ( x - 3 )
So either b is 3 or - 6 but it can't be negative so b is 3 and length is 6 cm
Hence verified