Question 206360
#1. Let n be the smaller number, then 4n is the larger number.
Their product is 16, so...
{{{n(4n) = 16}}}
{{{4n^2 = 16}}} Divide both sides by 4.
{{{n^2 = 4}}} Take the square root of both sides.
{{{highlight(n = 2)}}} and {{{highlight(4n = 8)}}}
#2. Start with the formula for the area of a rectangle of length = L and width = W.
{{{A = L*W}}} Substitute {{{L = W+3}}} and {{{A = 28}}}
{{{28 = (W+3)(W)}}} Simplify.
{{{28 = W^2+3W}}} Subtract 28 from both sides.
{{{W^2+3W-28 = 0}}} Factor this.
{{{(W-4)(W+7) = 0}}} Apply the zero product rule.
{{{W-4 = 0}}} or {{{W+7 = 0}}} so that...
{{{highlight(W = 4)}}} or {{{W = -7}}} Discard the negative solution as the width, W, can only be a positive value.
{{{L = W+3}}}
{{{highlight(L = 7)}}} 
The length is 7 feet and the width is 4 feet.