What is the perimeter of a 30°-60°-90° triangle that has a long leg of 9?

21.29 units

Step-by-step explanation:

30° 60° 90° triangles have a specific side ratio.

With respect to side a, x is side a, x√3 is side b, and 2x is side c.

Therefore the perimeter is the sum of these sides.

c is the long side so:

9 = 2x. x = 9/2 = 4.5.

x√3 = 4.5√3 ≈ 4.5 × 1.73 ≈ 7.79.

Perimeter = x + x√3 + 2x =

(9/2) + (9/2)√3 + 9 = 4.5 + 7.79 + 9 = 21.29.

Exact (27 + 9√3) / 2

Decimal: 21.29 [Nearest hundredth]

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