GF:
It makes a triangle, aka triangle GCF. It is a right triangle so we just need to find the hypotenuse to get GF.
a^2 + b^2 = c^2
Let’s plug in some values
(8)^2 + (15)^2 = c^2
8 is from GC and 15 is from FC
64 + 225 = c^2
289 = c^2
17 = c
GF = 17
NF:
NF is another hypotenuse but we are missing one of the legs of the triangle. We could fetch the numbers on the opposite of the square you can make
(EG and GC) and add them
8 + 16 = 24
Since the missing leg (NB) is equal to the side (AN) all we need is to divide 24 by 2
24/2 = 12.
Now let’s find the hypotenuse
(12)^2 + (5)^2 = c^2
(12 is NB and 5 is from BF)
144 + 25 = c^2
169 = c^2
13 = c
NF = 13
MG:
One again, MG is a hypotenuse and once again we are missing a leg. To get the leg we get the opposite sides (BF and FC) and subtract this total from AM
(5 + 15) - 8
20 - 8
12
Now let’s get the hypotenuse
(12)^2 + (16)^2 = c^2
(12 is from EM and 16 is from EG)
144 + 256 = c^2
400 = c^2
20 = c^2
MG = 20
ED:
ED is the final hypotenuse but now one of the legs is split up. To fix this we add the two line segment values (EG and CG)
16 + 8
24
Now let’s find the hypotenuse
(24)^2 + (7)^2 = c^2
(24 is from EC and 7 is from CD)
576 + 49 = c^2
625 = c^2
25 = c
ED = 25
*pen drop*
