Question 302231
Cutting the rectangle into half diagonally, it is a right angle triangle.

Using Pythagoras' Theorem: Length^2 + width^2 = Diagonal^2

Let's length = L , width = w and Diagonal = d 

L = (w + 1.6)cm and d = 8cm 

This gives: 

{{{(w+1.6)^2 + w^2 = 8^2}}}

{{{(w+1.6)^2 + w^2 = 64}}}

{{{(w^2 + 2(1.6)w + (1.6)^2) + w^2 = 64}}}

{{{2w^2 + 3.2w + 2.56 - 64 = 0 }}}


{{{2w^2 + 3.2w - 61.44 = 0 }}}

Using {{{w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} where 
a = 2 , b = 3.2 and c = -61.44 

w = 4.8 cm or - 6.4 (N/A)

and therefore, L = 4.8 + 1.6 = 6.4 cm

Answer: width = 4.8 cm and Length = 6.4 cm