DE = 48, EF = 54, and DF = 48 in this isosceles triangle.
For an isosceles triangle, two sides will be of equal length. In this case, since ΔDEF is isosceles and ∠E is the vertex, the sides DE and DF must be equal.
Given:
DE = 4x + 12
DF = 5x + 3
For an isosceles triangle, DE = DF:
4x + 12 = 5x + 3
Subtract 4x from both sides:
12 = x + 3
Subtract 3 from both sides:
x = 9
Now that we have found the value of x, let's substitute it back into the expressions for DE, EF, and DF to find their lengths:
DE = 4x + 12
DE = 4(9) + 12
DE = 36 + 12
DE = 48
EF = 7x – 9
EF = 7(9) – 9
EF = 63 – 9
EF = 54
DF = 5x + 3
DF = 5(9) + 3
DF = 45 + 3
DF = 48
So, DE = 48, EF = 54, and DF = 48 in this isosceles triangle.