Question

The circle is inscibed by the triangle. Find the perimeter of the triangle

Answer 1

where is it?

Answer 2

have you covered the 45-45-90 triangle ratios yet?

Answer 3

Yeah

Answer 4

notice this picture
that corner of the triangel, has 90 degrees
a circle has an "even radius" distance, meaning, the distance from the center of the circle
to the left and bottom sides, will be the same equal length
that equidistance, means that, if we draw a line from the center to the corner of it
it will be an angle bisector
meaning, it will make the 90 degrees corner, a 45-45 split
now, notice the triangles it makes, it makes two 45-45-90 degree ones

so the bottom part of the triangle is 2 + 5, given from the picture
you're just missing the other line on the left, that is "something" + 6

so, use the 45-45-90 ratios to get it

as far as the hypotenuse, or the slanted line in the triangle, you can just use pythagorean theorem for that

Answer 5

though, come to think, if the distances are the same, the side of the left segment, will be the same length at the bottom segment =)

so.. for that, yuo don't even need the 45-45-90 rule

Answer 6

\[\sqrt{8^2+7^2}+8+7=15+\sqrt{113}=25.6301 \]

Answer 7

Oh okay thanks :)

Answer 8

Your welcome.