Question 264741
Let {{{a}}} = the length in feet
Let {{{b}}} = the width in feet
Let {{{p}}} = perimeter in feet
The formula for perimeter is:
{{{p = 2a + 2b}}}
I'm given that {{{p = 280}}} ft
(1){{{280 = 2a + 2b}}}
Also given is:
(2){{{a = 4b + 20}}} ft
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Divide both sides of (1) by {{{2}}}, and
swap left and right
(1) {{{a + b = 140}}}
Subtract {{{4b}}} from both sides of (2)
(2) {{{a - 4b = 20}}}
Now subtract (2) from (1)
(1) {{{a + b = 140}}}
(2) {{{-a + 4b = -20}}}
{{{5b = 120}}}
{{{b = 24}}}
And, since
{{{a + b = 140}}}
{{{a + 24 = 140}}}
{{{a = 116}}}
The length is 116 ft and the width is 24 ft