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Question:-(Refer to the attachment).________... Answer with proper explanation required. ​

Answer»

Given,

  • AB = AC
  • AD is an angle bisector
  • AD = 2√2 cm

Since AB = AC, opposite ANGLES are ought to be equal.

\implies ABD = ACD

From Angle Sum Properly,

A + B + C = 180°

\implies 90° + ABD + ACD = 180°

\implies 2ABD = 90°

\implies ABD = ACD = 45° (ABC = ACB = 45°)

Now,

tan(ABD) = AD/BD

\longrightarrow tan45° = 2√2/BD

\longrightarrow BD = 2√2cm

Likewise, CD = 2√2cm.

We KNOW that, BC = BD + CD = 4√2cm

Now,

sin(ABC) = AC/BC

\longrightarrow sin45° = AC/4√2

\longrightarrow AC = 4√2/√2

\longrightarrow AC = AB = 4cm

For perimeter of ∆ABC,

AB + BC + AC

\longrightarrow 4 + 4 + 4√2

\longrightarrow (8 + 4√2) cm

Thus, the perimeter of ∆ABC is 8 + 4√2 cm.


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