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Please find the perimeter of the following shape (I know the answer, please explain steps)

Please find the perimeter of the following shape (I know the answer, please explain-example-1
User Nvrandow
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1 Answer

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Explanation:

the perimeter is the sum of all sides.

it is clearly a symmetric figure.

I assume the sqrt(36) is the whole baseline (incl. the left and right x).

so, we have

sqrt(8) + 2x = sqrt(36) = 6

1/2 × sqrt(8) + x = 3

sqrt(1/4 × 8) + x = 3

sqrt(2) + x = 3

x = 3 - sqrt(2)

to get the inclined sides we use Pythagoras

c² = a² + b²

c being the Hypotenuse, a and b being the legs of the right-angled triangle.

so,

side² = sqrt(8)² + (3 - sqrt(2))² = 8 + (9 - 6×sqrt(2) + 2) =

= 19 - 6×sqrt(2)

each inclined side is

sqrt(19 - 6×sqrt(2))

so, as perimeter we get

6 + sqrt(8) + 2×sqrt(19 - 6×sqrt(2)) =

= 15.3137085...

User Tawn
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