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As we know the right angle triangle with two equal side (isosceles) has side ratio in 1:1:root2 so according to question , the perimeter is 16+16root2 so the sides are 8root2:8root2:16 so the hypotenuse is 16
but the question asks hypotenuse.. hence the answer will be 16root2.
Neochronic , please check the detail before posting. you said 2x+root2*x = 16+16root2 in first part 2x is equal to 16, that means x = 8 and in second part root2*x is equal to 16root2, that means x = 16 hows that possible?
I have answered this Q but want to understand the way to solve this.
Isosceles triangle has :
Base = perpendicular = ab = bc Hypoteneous = ac
ac^2 = ab^2 + bc^2 ac^2 = ab^2 + ab^2 ac^2 = 2ab^2 ac = ab Sqrt(2) Perimeter of the triangle = ab+bc+ac 16+16(sqrt2) = ab+ ab + ab Sqrt (2) 16 + 8 (sqrt2) + 8 (sqrt2) = ab Sqrt (2) + ab + ab ab = bc = 8 (sqrt2) ac = 16