Question

What is the perimeter of a 30-60-90 triangle with a shortest side of 3?

Answer 1

Exact perimeter =
`9+3√(3)`

Approximate perimeter = 14.196152

Round that decimal value however needed.

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Step-by-step explanation

In a 30-60-90 triangle, the hypotenuse is twice the short leg.

In this case the hypotenuse is 2*3 = 6 units long.

In a 30-60-90 triangle, the long leg is
`√(3)` times as long compared to the short leg.

`\text{long leg} = (\text{short leg})*√(3)\\\\\text{long leg} = 3√(3)\\\\`

Add up the three sides to get the perimeter.

`\text{perimeter} = \text{side1}+\text{side2}+\text{side3}\\\\\text{perimeter} = \text{shortLeg}+\text{longLeg}+\text{hypotenuse}\\\\\text{perimeter} = 3+3√(3)+6\\\\\text{perimeter} = 9+3√(3)\\\\\text{perimeter} \approx 14.196152\\\\`