The square ABCD has a triangle with 3 sides on each side. 4。 5

ae=4， ef=3， af=5

ae⊥effec=∠eab

fec∽△aeb

Let the side length of the square be a

fe/ae=ce/ab=cf/be=3/4ce=3a/4

be=a/4

cf=3a/16

df=13a/16

In RT ADF, it is determined by the Pythagorean theorem:

a^2+(13a/16)^2=5^2

a = 16 root number 17 17

The side length of the square is 16 roots, 17 17

Because ae=4, ef=3, af=5, so ae*ae+ef*ef=af*af, so the triangle aef is a right triangle, and aef=90° so aeb+ cef=90°;

And because aeb+ b=90°, cef= b; and b= c=90°, so the triangle abe is similar to the triangle ecf;

So ab ce=ae ef=4 3

Let ab=4a, then ce=3a, be=a, in the triangle abe, ab*ab+be*be=ae*ae, so (4a)*(4a)+a*a=4*4*4

The solution is a=4 root number 17, 4a = 16 root number 17;

That is, the square side length is 16, and the number is 17;

4 4) 2 =8 because the area of the triangle is the base height of 2

The side lengths of similar triangles are proportional, so it can be concluded that the two long side ratios and the two short side ratios are equal, and let the short side be x, then there is.

x：3=15:5

and x=9, then the shortest side length of a1b1c1 is 9

Linking EF yields EPF=60° and PE=2 and PF=1 yields EF PF

PFC is an equilateral triangle, PF=PC=FC=1, so C1F=C1P=1, PBE is an equilateral triangle, PE=BE=BP=2, so B1P=2, FPB1=60°

So pf b1f

So pf surface b1ef

From the pf face b1ef to the surface aepf face b1ef as b1g ef, so b1g face aepf

Connecting AG, then B1AG is ab1 and the angle called by the surface AEPF is set to sin = B1G ab1

From the pf surface b1ef, ae pf can obtain ae surface b1ef, ae b1e, and ae=1, b1e=2

Get ab1 = 5

In b1ef, b1e=2, ef=b1f= 3, so b1g=2 2 3

So sin = b1g ab1 = 2 2 15 = 2 30 15