Question

Find the perimeter of a 30°-60°-90° triangle with a hypotenuse of 18

Answer 1

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Answer 2

This is a (relatively simple) 30-60-90 degree, or "right," triangle. Therefore, the Pythagorean Theorem applies.

I'd suggest you draw a picture of this 30-60-90 degree triangle and remember that the sides are often labeled Sqrt(3), 1 and 2, with 2 being the length of the hypotenuse, and Sqrt(3) and 1 being the length of the legs of the triangle.

You can find the lengths of the legs of the given triangle (the one with hypotenuse 18) by using proportions.

In the 30-60-90 triangle, the hypotenuse is 2. This is well worth memorizing.
In the larger, given triangle, the hyp. is 18.

therefore, you could choose either the longer or the shorter sides of both triangles and write another ratio.

supposing that you chose the shorter side, then the ratio of the shorter side 1 of the 30-60-90 triangle to the shorter side of the given triangle is 1:x.

Set these 2 ratios equal to one another and solve for x.

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Answer 3

im not looking for 30-60-90 /: