Question 178257
The width of a rectangular painting is two-thirds of its length. If the perimeter is 28ft, then what are the length and width?
:
Write an equation for each statement;
:
"The width of a rectangular painting is two-thirds of its length.
W = {{{2/3}}}L
:
" If the perimeter is 28ft,"
2L + 2W = 28
:
 then what are the length and width?
:
Substitute {{{2/3}}}L for W in the perimeter equation, Find L:
2L + 2({{{2/3}}}L) = 28 
2L + {{{4/3}}}L = 28
multiply eq by 3 to get rid of that annoying denominator, results:
6L + 4L = 3(28)
:
10L = 84
L= {{{84/10}}}
L = 8.4 ft 
:
Find W
{{{2/3}}}(8.4) = 5.6 ft
:
:
Check solution:
2(8.4) + 2(5.6) =
16.8 + 11.2 = 28 ft