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 = $\sqrt{ \dfrac{1}{3} }$
n = $\dfrac{ 1 }{ \sqrt{3} }$
Rationalization of root form
n = $\dfrac{1 }{ \sqrt{3}} \times \dfrac{\sqrt{3} }{ \sqrt{3}}$
n = $\dfrac{1}{3} \sqrt{3}$

The value of n is $\boxed{\dfrac{1}{3} \sqrt{3}}$