Question 548636
Start with the formula for the area of a rectangle:
{{{A = L*W}}} but the length, L, is given as:
{{{L = 2W-5}}} "The length...is 5 mm less than twice the width".
and the area, A, is given as {{{A = 9450}}} sq.mm., so...
{{{9450 = (2W-5)(w)}}} Simplify.
{{{2W^2-5W-9450 = 0}}} Solve this quadratic equation using the quadratic formula: {{{W = (-b+-sqrt(b^2-4ac))/2a}}}. a = 2, b = -5, and c = -9450
{{{W = (-(-5)+-sqrt((-5)^2-4(2)(-9450)))/2(2)}}} Evaluate this to get:
{{{W = 70}}} or {{{W = -67.5}}} Discard the negative solution as width is a positive quantity.
{{{W = 70}}}mm and...
{{{L = 2W-5}}}
{{{L = 140-5}}}
{{{L = 135}}}mm.