Question

A square contains three coloured Triangles find the length of blue line

Answer 1

length of blue line = 4√3  in A square containing three coloured Triangles of Equal Area

Step-by-step explanation:

Let say side of square = 4 + a

Area of green Triangle = (4 + a) * a /2

Area of Red Triangle =  (4 + a) * b /2   ( b is the height from base side to vertex)

(4 + a) * a /2 = (4 + a) * b /2  

=> b = a

Area of purple Triangle = (4) (4 + a - b) / 2

= 4 ( 4 + a - a) /2

= 4 * 4 /2

= 8

=> (4 + a) * a /2  = 8

=> (4 + a) * a = 16

=> a² + 4a= 16

Length of blue line = √ a² + (4 + a)²

= √ a² + 16 + a² + 8a

= √2a² + 8a + 16

= √2(a² + 4a) + 16

= √2(16) + 16

= √48

4√3

length of blue line = 4√3

Learn More

A square and an equilateral triangle have a side in common

https://brainly.in/question/744361

Find the area of the square EFGH​

https://brainly.in/question/11243961