Question 210959
Start with:
{{{A = L*W}}} Substitute A = 10 and L = W+4.
{{{10 = (W+4)*W}}} Simplify.
{{{10 = W^2+4W}}} Subtract 10 from both sides.
{{{W^2+4W-10 = 0}}} Use the quadratic formula to solve:{{{W = (-b+-sqrt(b^2-4ac))/2a}}} and a = 1, b= 4, and c = -10.
{{{W = (-4+-sqrt(4^2-4(1)(-10)))/2(1)}}} Evaluate.
{{{W = (-4+-sqrt(16-(-40)))/2}}}
{{{W = (-4+-sqrt(56))/2}}}
{{{W = (-4+-sqrt(4*14))/2}}}
{{{W = -2+sqrt(14)}}} or {{{W = -2-sqrt(14)}}}
{{{highlight_green(W = 1.74)}}} or {{{cross(W = -5.74)}}} Discard the negative solution.
The width is 1.74 feet and the length is 5.74 feet. (Approximately)