Question 857594
The diagonal splits the rectangle into 2
30-60-90 triangles. What you need to know
for this problem is the proportions of the sides.
(1) side opposite 30 degree angle: {{{ 1 }}}
(2) side opposite 60 degree angle: {{{ sqrt(3) }}}
(3) side opposite 90 degree angle: {{{ 2 }}}
( note that {{{ 1^2 + sqrt(3)^2 = 2^2 }}} )
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Now you can say:
{{{ a / 20 = 1 / 2 }}}
( short side of given triangle ) / ( diagonal of given triangle ) =
( ratio of short side / diagonal of all 30-60-90 triangles )
Multiply both sides by {{{ 20 }}}
{{{ a = 10 }}}
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And also:
{{{ b / 20 = sqrt(3) / 2 }}}
( long side of given triangle ) / ( diagonal of given triangle ) =
( ratio of long side / diagonal of all 30-60-90 triangles )
Again, multiply both sides by {{{ 20 }}}
{{{ b = 10*sqrt(3) }}}
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The perimeter, {{{P}}}, is:
{{{ P = 2a + 2b }}}
{{{ P = 2*10 + 2*10*sqrt(3) }}}
{{{ P = 20 + 20*sqrt(3) }}}
Hope this isn't confusing