Answer :
Final answer:
To find the perimeter of triangle DEF, we need to know the lengths of sides DE, DF, and EF. Given that D, E, and F are midpoints of sides BC, CA, and AB, respectively.The correct option is d. 6.4cm.
Explanation:
The perimeter of triangle DEF, we need to know the lengths of sides DE, DF, and EF. Since D, E, and F are midpoints of sides BC, CA, and AB, respectively, we can use the fact that midpoints divide a line segment into two equal parts.
Therefore, DE = BC/2, DF = CA/2, and EF = AB/2.
Given that the perimeter of triangle ABC is 12.8 cm, we can find the lengths of sides BC, CA, and AB by dividing the perimeter by 3. So, BC = CA = AB = 12.8/3 = 4.27 cm.
Substituting these values into the equations for DE, DF, and EF, we get DE = 4.27/2 = 2.135 cm, DF = 4.27/2 = 2.135 cm, and EF = 4.27/2 = 2.135 cm.
Finally, we can calculate the perimeter of triangle DEF by adding the lengths of its sides: Perimeter of △DEF = DE + DF + EF = 2.135 + 2.135 + 2.135 = 6.405 cm.
The correct option is d. 6.4cm.
