What is the relationship between the arches of the regular hexagons constructed on the sides of the right triangle below?

the sides correspond to lengths 3, 4, and 5

Explanation: We are given the areas A of the regular hexagons. The general formula for an area of such a hexagon is:

where a is the side length of the hexagon.

Use the formula to solve for a:

for the three hexagon areas we are given:

a = 5  (yellow)

a = 4  (blue)

a = 3  (red)

Please let me know whether this answers your question, or whether you were looking for another type of relationship statement

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step-by-step explanation:

just copy and paste it.

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{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1