Answer:
A
Step-by-step explanation:
Answer: 6x² + 36x + 22
Step-by-step explanation:2 faces (x + 3) by (x + 7), area of both these faces 2(x+3)*(x + 7)
2 faces (x + 3) by (x - 1), area of both these faces 2(x+3)*(x - 1)
2 faces (x -1 ) by (x + 7), area of both these faces 2(x-1)*(x + 7)
Whole surface area is
2(x+3)*(x + 7) + 2(x+3)*(x - 1) + 2(x-1)*(x + 7) =
=2(x² + 3x +7x +21) + 2(x² +3x -x - 3) + 2(x² - x +7x -7)=
=2x² + 20x +42 + 2x² + 4x - 6 + 2x² + 12x -14 =
= 6x² + 36x + 22
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.