Question

A rectangle with a length 3 cm and width 3n^2-2 cm has an area of -3n cm^2. What value might n have?

Answer 1

Area of rectangle could be determined with
a = l × w

plug in the algebraic expression into the formula
l × w = a
3 × (3n² - 2) = -3
9n² - 6 = -3
9n² = -3 + 6
9n² = 3
divide both side by 3
3n² = 1
n² = 1/3
n =
`\sqrt{ (1)/(3) }`
n =
`( 1 )/( √(3) )`
Rationalization of root form
n =
`(1 )/( √(3)) * (√(3) )/( √(3))`
n =
`(1)/(3) √(3)`

The value of n is
`\boxed{(1)/(3) √(3)}`