If the perimeter of an isosceles right triangle is 16 + 16 2 inches lo

We know that a perpendicular needs to be find out.
\(16 + 16 \sqrt{2}\) can be perimeter of an isosceles triangle only when 16 is the largest side(sum of any two sides will be larger than the third side).
and \(16 \sqrt{2} > 16\)
Hence two sides of same length = 2x = \(16 \sqrt{2}\)
x = \(8 \sqrt{2}\)
Let the largest side = s

perimeter = 2x + s
Taking a perpendicular on s of length h, we have a right triangle with sides x(hypotenuse), \(\frac{s}{2}\) and h.
From here we can either use pythagoras theorem to find out h. OR
As we know, if in a right triangle the hypotenuse is of the form \( \sqrt{2}a\) then other two side are equal of length 'a'.

Hence \(8 \sqrt{2}\) gives h = 8.

Answer D.