Respuesta :
Answer:
The longest side is 330.9 units.
Step-by-step explanation:
Since the triangles are similar, the ratio of the corresponding sides of two triangles is equal.
In other words,
[tex]\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}[/tex]
The lengths of the sides of triangle ABC are
AB = 140 , BC = 120 , CA = 110
The length of smallest side of triangle DEF is 260.
Thus, [tex]\frac{CA}{FD} = \frac{110}{260} = \frac{11}{26}[/tex]
thus,
[tex]\frac{AB}{DE} = \frac{11}{26} = \frac{140}{DE}[/tex]
So, DE = 330.9 units
similarly,
[tex]\frac{BC}{EF} = \frac{11}{26} = \frac{120}{EF}[/tex]
So, EF = 283.636 units
Thus the sides of triangle are 260, 283.636 and 330.9 units.
The longest side is 330.9 units.
