Question

What is the perimeter of triangle KLM? i was only given one side and then 60° and 30°

please help this makes no sense

Answer 1

`18+6√(3)`

Explanation:

In all 30-60-90 triangles, the side lengths are in the ratio
`x:x√(3):2x`, where
`2x` is the length of the hypotenuse, or longest side, of the triangle and
`x` is the length of the side that is directly opposite to the 30 degree angle.

The figure consists of three 30-60-90 right triangles (two inside a larger one). The side KL is marked as 6 meters and represents the side opposite to the 30 degree angle of the largest triangle (Since
`\angle L=90^(\circ)` and
`\angle K=60^(\circ)`). Therefore, the hypotenuse (longest side) of the triangle must be
`2\cdot 6=12` and the other leg must be
`6√(3)`.

The perimeter of a polygon is equal to the sum of all the polygon's sides and therefore the perimeter of thing triangle is
`6+12+6√(3)=\boxed{18+6√(3)}`