Answer:
m+n = 337
Step-by-step explanation:
Lets start from the first triangle, It is given to be as 30-60-90.
The hypotenous of first rectangle be 2x, then other sides are by default x and
, using laws of trigonometry.
(sin(30) = 0.5 and cos(30) = )
The perimeter of first triangle is ,
=
Now, for second triangle, the longer leg is 2x, and similarly again,
other 2 sides are .
Again the perimeter of triangle comes out as,
=
Thus, the repeating pattern is identified. The consecutive perimeters differ by, multiplying by factor
Thus, we can say that perimeter of 4th triangle is,
= , where X is the repeating constant.
And of 12th triangle is,
= ,
Evaluating the above ratio, we get,
=
Thus, m =256 and n=81.
Thus, m+n = 256+81 = 337.