Question 1203272: What is the perimeter of an equilateral triangle if it’s altitude measures 2√3cm Found 3 solutions by josgarithmetic, ikleyn, greenestamps:Answer by josgarithmetic(39625) (Show Source):
You can put this solution on YOUR website! Draw what is described. You can identify two congruent special right-triangles.
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perimeter is 12 cm.
You can put this solution on YOUR website! .
What is the perimeter of an equilateral triangle if it’s altitude measures 2√3cm
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Let "a"be the length of the side of this equilateral triangle.
For any equilateral triangle, there is well known expression for the height
h = .
Hence, in our case = .
It gives for "a" a = .
Hence, the perimeter is 3a = 3*4 = 12 cm. ANSWER.
You can use the "well-known expression" for the side length of an equilateral triangle in terms of the length of the altitude if you have a love of formulas.
For me that formula is litter for clouding the mind, since the problem is easily solved by simple analysis.
The altitude of an equilateral triangle divides the triangle into two 30-60-90 right triangles, in which the altitude is the long leg and the side length of the triangle is the hypotenuse.
Using the basics of the 30-60-90 right triangle, if the long leg has length , then the short leg has length 2 and the hypotenuse has length 4.
ANSWER: The side length is 4, so the perimeter is 12.
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