dave13 wrote:
AbdurRakib wrote:
In the figure shown,PQRSTU is a regular polygon with sides of lenght x.What is the perimeter of triangle PRT in terms of x?
A. (\(x\sqrt{3}\))/2
B. \(x\sqrt{3}\)
C. (3\(x\sqrt{3}\))/2
D. 3\(x\sqrt{3}\)
E. 4\(x\sqrt{3}\)
OG Q 2017(Book Question: 145)
generis hello
i have one awesome question
one thing i dont get why are you dividing by two ? by drawing a perpendiculat line we create a right triangle 30 60 90, we are not dividing right triangle, we create it
no ?
Any idea
niks18 ?
dave13 :
niks18 , apparently able
to get a word in edgewise
addressed what to do
with a "2" that is now "1."
I'm hoping a third ratio is also clear, see below.
That ratio also must be divided by 2.
sadikabid27 , maybe this discussion or this post will help.
See below for a link to 30-60-90 triangle overview.
dave13 , yes, we create two identical 30-60-90 triangles at vertex U.
So let's take
niks18 's answer and line up the ratios.
Normal = \(30: 60 : 90\)
Normal = \(1 : \sqrt{3} : 2\)Normal = \(x : x\sqrt{3} : 2x\)But we can't call long sides PU and UT "2x" or "2."
Both are hexagon sides.
Hexagon side length is
not \(2x\) or \(2\)
It is \(x\). Or, if you're thinking in numeric multiples, \(1\)
2x or 2 got divided by 2.
What you do to one part of a ratio,
you must do to all parts.
Divide all ratio parts by 2
\(30 : 60 : 90\)
Adjusted = \(\frac{1}{2} : \frac{\sqrt{3}}{2} : 1\)Adjusted = \(\frac{x}{2} : \frac{x\sqrt{3}}{2} : x\)Length of ONE side of the big triangle =
\(\frac{x\sqrt{3}}{2} + \frac{x\sqrt{3}}{2} = x\sqrt{3}\)Hope that helps.
P.S. For a quick review of 30-60-90 triangles as well as an interesting proof see HERE.
dave13 - last thing . . . one part of the answer you quoted may have confused you.
I wrote Regular hexagon, 120 degrees at each vertex, equilateral triangle
Highlight refers to the big triangle in the center, not the smaller right triangles we create.
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