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prity

· started a discussion

· 1 Months ago

please provide detail solution (Question: 107650.0 )

what is 30-60-90 theorem???

Question:
An equilateral triangle circumscribes all the six circles, each with radius 1 cm. What is the perimeter of the equilateral triangle?

Options:
A) 6(2+\(\sqrt{3}\)) cm
B) 3(\(\sqrt{3}\) + 2)  cm
C) 12(\(\sqrt{3}\)+4) cm
D) None of the above
Solution:
Ans: (a) 


DE = GH = 4, \(\angle \)ADG = 60°

Then from 30 - 60 - 90 theorem

AG = \(\sqrt[]{3},\ BH\ = \sqrt[]{3},\) then

AB = AG+GH+BH

Then perimeter of \(\triangle\)ABC = \(3\times \left ( \sqrt[]{3}+4+\sqrt[]{3} \right )=3\times \left ( 2\sqrt[]{3}+4 \right )=6\left ( \sqrt[]{3}+2 \right )\)

Knowledge Expert

· commented

· 1 Months ago

A 30-60-90 triangle is special because of the relationship of its sides. Hopefully, you remember that the hypotenuse in a right triangle is the longest side, which is also directly across from the 90 degree angle. It turns out that in a 30-60-90 triangle, you can find the measure of any of the three sides, simply by knowing the measure of at least one side in the triangle.
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