Question

The pink triangle is equilateral and grids are unit squares. How long is the red line?

Answer 1

Given : The pink triangle is equilateral and grids are unit square

To Find :   Red line length

Solution:

Perpendicular Height of red line is  2 unit

Width / base  of red line is 3 unit  - (1/2) of triangle base

Let say triangle base is  2b   units

Then Width / base  of red line is   3 - b  unit

Now if base of equilateral triangle is  2b  units

then 2b² - b²  = 1²   ( as height of triangle is 1 unit )

=> 3b² = 1

=> b² = 1/3

⇒ b = 1/√3

Then Width / base  of red line is   3 - 1/√3  unit

Height is 2 unit

Length of red line = √(2²  + ( 3 - 1/√3)² )

√(4 + 9 + 1/3 - 2√3)

= √(40/3 - 2√3)

= 3.141533   units

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Answer 2

Answer:

Given : The pink triangle is equilateral and grids are unit square

To Find :   Red line length

Step-by-step explanation:

Solution:

Perpendicular Height of red line is  2 unit

Width / base  of red line is 3 unit  - (1/2) of triangle base

Let say triangle base is  2b   units

Then Width / base  of red line is   3 - b  unit

Now if base of equilateral triangle is  2b  units

then 2b² - b²  = 1²   ( as height of triangle is 1 unit )

=> 3b² = 1

=> b² = 1/3

⇒ b = 1/√3

Then Width / base  of red line is   3 - 1/√3  unit

Height is 2 unit

Length of red line = √(2²  + ( 3 - 1/√3)² )

√(4 + 9 + 1/3 - 2√3)

= √(40/3 - 2√3)

= 3.141533   units