pythagoras' Theorem

1: a^2+12^2=13^2(Pyth. theorem)
a^2=169-144
a=5;
13^2+(2a)^2=b^2(Pyth. theorem)
b^2=169+100
b=√269 =16.4(corr.to 3 sig.fig.);
2: x^2+9^2=15^2(Pyth. theorem)
x^2=225-81
x=12;
FE=BC=20;
ED+20+12=41
ED=9;
CE=BF=9;
y^2=9^2+9^2(Pyth. theorem)
y^2=162 y=√162 =12.7(corr. to 3 sig.fig.)
3: AC^2=5^2+1^2(Pyth. theorem)
AC^2=26
AC=√26;
AC^2+1^2=y^2(Pyth. theorem)
y^2=26+1
y=√27 =5.20(corr.to 3 sig.fig.)

1
AD^2+CD^2=AC^2
12^2+a^2=13^2
a=5
AB^2+AC^2=BC^2
(2*5)^2+13^2=B^2
b=16.4

2
AF^2+BF^2=AB^2
x^2+9^2=15^2
x=12
CE^2+ED^2=CD^2
9^2+(41-20-12)^2=CD^2
CD=12.7

3
√(5^2+1^2)^2+1^2=y
y=27