Answer:
16[tex]\sqrt{2}[/tex]
Step-by-step explanation:
note that in a 45° - 45° - 90° triangle the legs are equal in length, since triangle is a right isosceles
let x be the length of the leg
using Pythagoras' identity on the triangle, then
x² + x² = 32²
2x² = 1024 ( divide both sides by 2 )
x² = 512 ( take the square root of both sides )
x = [tex]\sqrt{512}[/tex] = 16[tex]\sqrt{2}[/tex]
the legs have length 16[tex]\sqrt{2}[/tex]
