Question 294591
Use the Pythagorean theorem: {{{c^2 = a^2+b^2}}} where c = 10, a = L, and b = W
{{{10^2 = L^2+W^2}}} Substitute {{{L = W+2}}}
{{{100 = (W+2)^2+W^2}}}
{{{100 = (W^2+4W+4)+W^2}}} Rearrange into a standard form for quadratice equations.
{{{2W^2+4W-96 = 0}}} Factor 2.
{{{2(W^2+2W-48) = 0}}} so...
{{{W^2+2W-48 = 0}}} Solve by factoring.
{{{(W-6)(W+8) = 0}}} Apply the "zero product" rule.
{{{W-6 = 0}}} or {{{W +8 = 0}}} which means that...
{{{W = 6}}} or {{{W = -8}}} Discard the negative solution.
{{{W = 6}}} This is the width of the rectangle.