Question 250839
we need two formulas:
{{{P = 2L + 2W}}}
{{{A = LW}}}.
From our given information we have
(i) {{{42 = 2L + 2W}}}
(ii) {{{104 = LW}}}
Solve equation (ii) for L.
(iii) {{{L = 104/W}}}
Substitute (iii) information into (i) to get
(iv) {{{42 = 208/W + 2W}}}
or
(v) {{{21 = 104/W + W}}}
Now multiply both sides by W to get
{{{21W = 104 + W^2}}}
set this equal to 0 and factor.
{{{w^2 - 21W + 104}}}
{{{(W-13)(W-8) = 0}}}
W = 13, W = 8.
If W = 13m, then L = 8m.
If W = 8m, then L = 13m.