Question 180990
Find the perimeter of a triangle if one side is 16 feet, another side is two-seventh the perimeter, and the third side is one-third the perimeter?
;
let p = the perimeter
:
p = {{{2/7}}}p + {{{1/3}}} + 16
Multiply equation by a common multiple of 7 and 3
21(p) = 21*{{{2/7}}}p + 21*{{{1/3}}} + 21(16)
Cancel the denominators, results:
21p = 3(2p) + 7(p) + 336
21p = 6p + 7p + 336
21p = 13p + 336
21p - 13p = 336
8p = 336
p = {{{336/8}}}
p = 42 ft is the perimeter
;
:
Check solution:
p = {{{2/7}}}(42) + {{{1/3}}}(42) + 16
p = 12 + 14 + 16
p = 42