we have an isosceles right triangle, because both angles are 45
with the hypothenuse of 16
it is a special triangle
we know that a^2+b^2=c^2
for us, a=b
c^=2a^2
c=a * sqrt 2
a=16/(sqrt2)
a= 8 sqrt 2 this is AB
it is your 4th choice
to find BD
we have a right triangle, with a hyp = 8sqrt2
one side =8
we use the same
a^2+b^2=c^2
128-64=64
a=sqrt64=8
BD=8 and AB is 8sqrt 2
![16=a\sqrt[]{2}](https://img.qammunity.org/2023/formulas/mathematics/college/pxz7d129uxpy4c3xxu1e4yrohof4vcnihk.png)