Answer:
The length of the longest section x = 36 ft
Step-by-step explanation:
Total length of the wire = 51 ft
Let first section of wire = x
Second section of wire = y
Third section of wire = z
According to given data
x = 3 y & y = 4 z
Total length of the wire = x + y + z = 51
y = 12
x = 3 × 12 = 36
Therefore the length of the longest section x = 36 ft
Given that ∠B ≅ ∠C.
to prove that the sides AB = AC
This can be done by the method of contradiction.
If possible let AB =AC
Then either AB>AC or AB<AC
Case i: If AB>AC, then by triangle axiom, Angle C > angle B.
But since angle C = angle B, we get AB cannot be greater than AC
Case ii: If AB<AC, then by triangle axiom, Angle C < angle B.
But since angle C = angle B, we get AB cannot be less than AC
Conclusion:
Since AB cannot be greater than AC nor less than AC, we have only one possibility. that is AB =AC
Hence if angle B = angle C it follows that
AB = AC, and AB ≅ AC.