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secondary 2 | Maths
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Pls help me i do not understand this question thank youu soo much
Date Posted: 3 years ago
Views: 287
Have you learnt the Pythagoras Theorem yet?
Angle POQ is 90 degrees, if you work it out. I use triangle POQ instead of the smaller ones for simplicity.
PO = OQ = r
Hypotenuse PQ = L
By the Pyth. Thm,
L^2 = r^2 + r^2
L^2 = 2r^2
L = sqrt (2r^2)
L = sqrt 2 * sqrt r^2
L = r * sqrt 2
Angle POQ is 90 degrees, if you work it out. I use triangle POQ instead of the smaller ones for simplicity.
PO = OQ = r
Hypotenuse PQ = L
By the Pyth. Thm,
L^2 = r^2 + r^2
L^2 = 2r^2
L = sqrt (2r^2)
L = sqrt 2 * sqrt r^2
L = r * sqrt 2
Perimeter of the square
= 4 L
= 4 r sqrt 2
= (4 sqrt 2) * r
Circumference of circle
= 2 pi r
= (2 pi) * r
Our eyes can obviously tell us that the perimeter of the square is smaller than the circumference of the circle. So...
4 sqrt 2 < 2 pi
sqrt 2 < pi/2
Both sqrt 2 and pi are real, but irrational, numbers.
= 4 L
= 4 r sqrt 2
= (4 sqrt 2) * r
Circumference of circle
= 2 pi r
= (2 pi) * r
Our eyes can obviously tell us that the perimeter of the square is smaller than the circumference of the circle. So...
4 sqrt 2 < 2 pi
sqrt 2 < pi/2
Both sqrt 2 and pi are real, but irrational, numbers.
'our eyes can tell' won't be a sufficient explanation for why the perimeter of the square is smaller than the circumference of the circle
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Hi Hii, draw on the diagram all that you know.
Date Posted:
3 years ago
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