Question

The sides of right triangles are calculated. Using this, calculate the perimeter of the
angles given below.

Find the perimeter of triangle ABC​

Answer 1

Solution :-

In right angled ∆ADB, we have,

→ ∠ABD = 30°

→ AD = 1 .

so,

→ sin 30° = AD/AB

→ (1/2) = 1/AB

→ AB = 2

and,

→ tan 30° = AD/BD

→ (1/√3) = 1/BD

→ BD = √3

similarly, In right angled ∆ADC, we have,

→ ∠ACD = 30°

→ AD = 1 .

so,

→ sin 30° = AD/AC

→ (1/2) = 1/AC

→ AC = 2

and,

→ tan 30° = AD/CD

→ (1/√3) = 1/CD

→ CD = √3

then, In ∆ABC we have,

→ AB = 2

→ AC = 2

→ BC = BD + DC = √3 + √3 = 2√3

therefore,

→ Perimeter of ∆ABC = AB + AC + BC = 2 + 2 + 2√3 = 4 + 2√3 = 2(2 + √3) .

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