Answer:
[tex]\displaystyle 36\:units[/tex]
Step-by-step explanation:
Split up this Isosceles, Right Triangle into two congruent smaller right triangles. The reflexive side [the line that splits them apart] is 6 units, and both legs are 8 units, leaving the hypotenuses to AUTOMATICALLY be 10 units, according to the Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 6^2 + 8^2 = 10^2 \\ \\ 36 + 64 = 100 \\ \\ 100 = 100[/tex]
With this Pythagorean Triple, we know that our dimensions are correct. Now, to find the perimeter, just add up all the sides EXCEPT for the divider:
[tex]\displaystyle 2[10] + 2[8] = 20 + 16 = 36[/tex]
I am joyous to assist you anytime.
