Problem Solving

Hi answers goes this way ,.

the three sides of the isoscles triangle are( 1:1:Sq root 2)

assume them to be a,a,b

therefore a+a+b= 16+ 16 sqrt 2

2a+b = 16+ 16 sqrt 2 ---------------------------- i

we know hypt^2= base ^2 + height ^2
=> b^2= a^2+a^2

b= Sq rt 2 a ----------------------------------- ii

substitute ( ii) in (i)

2a +sqrt 2a= 16+ 16 sqrt 2

a = 8 sqrt 2

there hypotenuese = sqrt ( ( 8 sqrt 2)^2 + (8 sqrt 2)^2 )

there fore 16.