Question

Simple Math Puzzle on triangles.

ABCD is a square. Green circle's radius = 2 cm. Blue circle has a radius = 4 cm.
Find the length "a" of the edge of the square.

Use the formulas related to triangles.

Answer 1

ANSWER =
...................
PF = KF = 4CM

Perimeter OF BFC = BP
+ PF
+ KF
+ KC
+ BC
Perimeter [ BFC ] = ( BT + CT ) + PF + KF + BC
Perimeter [ BFC ] = a + a + 4 + 4
 Perimeter [ BFC ] = 2a + 8

AND
...............

16[ 2a + 8 ]/2 + 16 = a²
16a + 64 + 16 = a²
a² - 16a - 80 = 0
a = 20, -4

$= = = = = = = = = = = =$

Answer 2

Nice question.
Answer explained below.
Comment below if any doubt occurs to you.