Question

Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.

What are the missing segment lengths in the image?
12√3
24
12√2
12
45
E
45°
12
24√3 24√2
45°
45°

Answer 1

DF=12√2

FG=12√2

DG=24

Explanation:

Ratio of special Right Triangle (45:45:90): x:x:x√2

Triangle DEF: x:x:x√2

x=12

12: 12: 12√2

So, DF= 12√2

Opposite (if q, then p) Base angle theorem. So, FD≅FG.

FD=12√2

FG=12√2

Ratio of 45:45:90 Triangle: x:x::x√2

x in triangle FDG= 12√2

12√2:12√2:12√2(√2)

12√2*√2=24

=12√2: 12√2: 24

DG=24