Question

the perimeter of a triangle is 187 feet. the longest isde of the triangle is 12 feet shorter than twice the shortest side. the sum of th lengths of th etwo shorter sides is 35 feet more than the length of the longest side. find the lengths of the sides of the triangle

Answer 1

`\mathrm{43ft,\ 76ft\ and\ 68ft}`

Explanation:

`\mathrm{Let\ the\ shortest\ side\ of\ the\ triangle\ be\ x.\ Then,\ the\ longest\ side\ of\ the\ triangle}\\\mathrm{will\ be\ 2x-10.}\\\mathrm{Let\ the\ length\ of\ remaining\ side\ of\ the\ triangle\ be \ y.}\\\mathrm{Given,}\\\mathrm{Sum\ of\ two\ shorter\ sides=35+longest\ side}\\\mathrm{or,\ x+y=35+(2x-10)}\\\mathrm{or,\ y=25+x........(1)}\\\mathrm{Also\ we\ have}\\\mathrm{Perimeter\ of\ triangle=187ft}\\\mathrm{or,\ x+(2x-10)+y=187}\\\mathrm{or,\ 3x+y=197}\\\mathrm{or,\ y=197-3x...........(2)}`

`\mathrm{Equating\ equations\ 1\ and\ 2,}\\\mathrm{25+x=197-3x}\\\mathrm{or,\ 4x=172}\\\mathrm{or,\ x=43ft}\\\mathrm{i.e.\ length\ of\ shortest\ side=43ft}\\\mathrm{Now,\ length\ of\ longest\ side=2x-10=2(43)-10=76ft}\\\mathrm{Finally,\ length\ of\ third\ side=y=25+x=68ft}`

`\mathrm{So,\ the\ required\ lengths\ of\ triangle\ are\ 43ft,\ 76ft\ and\ 68ft.}`