When using units with algebra, ensure that:
• the units used are consistent throughout, and
• that the units are manipulated along with the calculation.
For example, `x` cm x `y` mm should be changed to 10`x` mm x ``mm, which is equal to `10xytext( cm)^2`.
1. What is the volume of a cuboid that is `5x` cm long, `3x` cm wide and `2x` cm high?
Answer: `30x^3text( cm)^3`
Multiply the numbers together: 5 x 3 x 2 = 30
Multiply the `x` values together for `x^3`
The measurements are also multiplied together; cm x cm x cm = cm3
2. The area of a rectangle is 115.2 cm2. The length of the rectangle is `x` cm, and the width of the rectangle is `8x` mm. What is `x`?
Answer: `x = 12`
Note that the width is in millimetres. Convert mm to cm: width is `0.8x` cm
`115.2 = x text( cm) times 0.8x text( mm)`
`115.2 = 0.8x^2`
`144 = x^2`
`x = 12`