Question 68680
Starting with the formula for the area of a rectangle: {{{A = L*W}}} which is given as 105 sq.cm., you can substitute x for W and (2x+1) for L to get:
{{{(2x+1)(x) = 105}}} Simplify and solve for x.
{{{2x^2+x = 105}}} Subtract 105 from both sides of the equation.
{{{2x^2+x-105 = 0}}} Factor this quadratic equation.
{{{(2x+15)(x-7) = 0}}} Apply the zero product principle.
{{{2x+15 = 0}}} and/or{{{x-7 = 0}}} from which you get:
{{{2x+15 = 0}}} Subtract 15 from both sides.
{{{2x = -15}}}} Divide both sides by 2.
{{{x = -(7.5)}}} Discard this negative solution as the width must be a positive value.
{{{x-7 = 0}}}
{{{x = 7}}}
The width is 7 cm.
The length is 2x+1 = 2(7)+1 = 15 cm.
The perimeter is:
{{{P = 2L + 2W}}}
{{{P = 2(15)+2(7)}}}
{{{P = 30+14}}}
{{{P = 44}}} cm.