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2 years ago

Find the ratio of the areas.

Mathematics

1 answer:

pshichka [43]2 years ago

3 0

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

_____

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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Step-by-step explanation:

Circle Theorem vocabulary

Chord: a straight line joining two points on the circle.
Inscribed angle: the angle formed (vertex) when two chords meet at one point on a circle.
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Therefore:

$\displaystyle \angle RST=\dfrac{1}{2} \overset{\frown}{RT}$

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2 years ago

The length of a rectangle is three times the width. the perimeter is 44 cm what are the dimension of the rectangle

Vlada [557]

We know that the perimeter is 44, and perimeter is 2l + 2w.
2l + 2w = 44

We also know that the length, which I will call l, is three times the width, which I will call w.d
l = 3w

Let's rearrange this so it matches the first equation.
l - 3w = 0

Now we can set up a system of equations:
2l + 2w = 44
l - 3w = 0

Multiply the second equation by -2 so we can get the l's to cancel

2l + 2w = 44
-2l + 6w = 0

Now add them together and solve for w.
8w = 44
w = 5.5

Knowing w, we can solve for l using either original equation.
l = 3w
∴ l = 3(5.5)
l = 16.5

To check this, we can substitute the numbers back into the original equation:
2(16.5) + 2(5.5) = 44
16.5 = 3(5.5)

So the dimensions of the rectangle are 16.5 x 5.5

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3 years ago