Question 129109
Start with the formula for the area of a rectangle:
{{{A = L*W}}}
You are told that the width, W is 3 ft. less than the length, L, so this can be written as:
{{{W = L-3}}} so now you can replace W with (L-3) and write:
{{{A = L*(L-3)}}} and you are also told that the area is 154 sq.ft., so...
{{{L*(L-3) = 154}}} Simplify.
{{{L^2-3L = 154}}} Subtract 154 from both sides.
{{{L^2-3L-154 = 0}}} There's your quadratic equation and it can be solve by factoring.
{{{(L-14)(L+11) = 0}}} Applying the zero products principle, we get:
{{{L-14 = 0}}} or {{{L+11 = 0}}} so that...
{{{L = 14}}} or {{{L = -11}}} Use only the positive value as lengths are positive quantities.
{{{L = 14}}} and...
{{{W = L-3}}}
{{{W = 14-3}}}
{{{W = 11}}}
The dimensions of the rectangle are:
Length = 14 ft. and width = 11 ft.
Check:
{{{A = L*W}}}
{{{A = 14*11}}}
{{{A = 154}}}sq.ft.