Question

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?

Answer 1

 If it is parallel to the hypotenuse, then the hypotenuse is twice as long. So h = 8x 
Then the legs will be (8x)/sqr(2). Since the triangle is a 45-45-90 

So the perimeter = 8x + (8x)/sqr(2)+ (8x)/sqr(2) 
=8x+ 16x/sqr(2) 
=8x+ 8xsqr2 

2)if the midsegment Is parallel to a leg, then each leg = 8x and the hypotenuse = 8x sqr2 

Then the perimeter is 8x + 8x + 8xsqr2 
= 16x+ 8xsqr2