Right isosceles triangle abc has a hypotenuse of length h.
line segment de is a midsegment with length 4x.
what is the perimeter of triangle abc?

a. 16x+h
b. 12x
c. 8x+h
d. 24x

The answer is a. 16x+h

Since a triangle is isosceles, its both legs are the same. So, we have two sides and a hypotenuse (a, a, and h)
A midsegment length (m) of a triangle is a half of a parallel bottom leg of the triangle (a):
a = 2m

The perimeter (P) of the triangle is the sum of its sides:
P = a + a + h

It is given:
m = 4x
Since a = 2m, we have:
a = 2*4x = 8x

Therefore, the perimeter is:
P = a + a + h = 8x + 8x + h = 16x + h

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