Mathematics Question and Solution
Let x be the side of the small inscribed square.
Calculating x.
Notice;
The side length of the ascribed square is 14 cm.
A small triangle with height ½ cm on the same vertical length with AC and extends from C, and hypotenuse 0.69047619048 cm is attached to the quadrilateral inscribed square ACDE, that have the small square inscribed to make the small square inscribed a right-angled triangle with adjacent sides 10.5 cm and 10 cm, and hypotenuse 14.5 cm.
The interior angles of the right-angled triangle are;
atan(20/21)°, (90-atan(20/21)° and 90°.
Therefore x, the side of the small inscribed square is;
x+xtan(90-atan(20/21))+xtan(atan(20/21)) = 14.5
= 3.00238095238x = 14.5
x = 4.82950039651 cm
Or
x = 29/6 cm.
It implies;
Perimeter of the inscribed small square is;
4(29/6)
= ⅓(58) cm.
Or
4(4.82950039651)
= 19.318001586 cm.
