Full answer to: The area of a rectangle is 2m^2. If the width of the rectangle is (2-sqr3) m, what is the length of the rectangle? Express your answer with a rational denominator.

Answer 1

Area =LW =2 = L(2-sqr3)

L = 2/(2-sqr3)

multiply numerator and denominator by the conjugate of 2-sqr3

it's the same as multiply by 1, which doesn't change the value of the fraction

= [2/(2-sqr3)][(2+sqr3)/(2+sqr3)]

= 2(2+sqr3)/(4-3) = 4+2sqr3

Length = 4+2sqr3

L= about 4+2(1.732) = about 7.46

W =2-sqr3 = 2-1.732= about 0.268

LW = (7.46)(0.27) = about 2.01