Find the ratio of the areas.
1 answer:
9514 1404 393
Answer:
3 -2√2
Step-by-step explanation:
For a regular octagon of side length s, the "flat-to-flat" dimension across the center is s(1+√2). The flat-to-flat dimension of the shaded center octagon is simply s. The ratio of areas is the square of the ratio of linear dimensions, so we have ...
small area / large area = (1/(1+√2))^2 = 1/(3+2√2)
small area/large area = 3 -2√2
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The attachment shows octagons after the fashion described here. The side length of the larger one is 2 units. The numbers inside are the areas. They have the ratio shown above.
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For a better understanding of the solution provided here, please find the diagram attached.
In the diagram, ABCD is the room.
AC is the diagonal whose length is 18.79 inches.
The length of wall AB is 17 inches.
From the given information, we have to determine the length of the BC, which is depicted a , because for the room to be a square, the length of the wall AB must be equal to the length of the wall BC.
In order to determine the length of the wall BC, or , we will have to employ the Pythagoras' Theorem here. Thus:
Thus, inches
and hence, the given room is not a square.
