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Perimeter = 276
Ratio = 5:8:10
1.- Sum up the numbers of the proportion
5 + 8 + 10 = 23
2.- Divide the perimeter by the previous result
276/23 = 12
3.- Calculate the length of the longest side
length = 12 x 10 = 120
4.- Result, the length of the longest side = 120 in