Sagot :
Bonjour,
1) 0 < x < 6
2) d'après le théorème de Thalès : RH/RM = RS/RT = SH/TM
donc : RH/10 = x/6 = SH/8
donc : RH = 10 × (x/6) = 10x/6 = 5x/3
et SH = 8 × (x/6) = 8x/6 = 4x/3
3) périmètre RSH = RS + SH + RH
= x + 4x/3 + 5x/3
= (3x+4x+5x)/3
= 12x/3
= 4x
4) périmètre SMTH = ST + TM + HM + SH
= (RT-RS) + TM + (RM-RH) + SH
= (6 - x) + 8 + (10 - 5x/3) + 4x/3
= 6 - x + 8 + 10 - 5x/3 + 4x/3
= 6 + 8 + 10 - x - 5x/3 + 4x/3
= 24 - 3x/3 - 5x/3 + 4x/3
= 24 - 4x/3