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alexandr402 [8]
3 years ago
13

What is the similarity ratio for two circles with areas 2π m2 and 200π m2?

Mathematics
2 answers:
andreyandreev [35.5K]3 years ago
8 0

Answer:  The required similarity ratio is 1 : 10.

Step-by-step explanation:  We are given to find the similarity ratio for the two circle with areas as follows:

A_1=2\pi~\textup{m}^2,\\\\A_2=200\pi~\textup{m}^2.

Finding a similarity ratio for two circles is equivalent to finding the ratios of their radii.

Let, r_1 and r_2 be the radii of the two circles with areas A_1 and A_2 respectively.

So, we have

\dfrac{A_1}{A_2}=\dfrac{2\pi}{200\pi}\\\\\\\Rightarrow \dfrac{2\pi r_1^2}{2\pi r_2^2}=\dfrac{1}{100}\\\\\\\Rightarrow \dfrac{r_1^2}{r_2^2}=\dfrac{1}{100}\\\\\\\Rightarrow \dfrac{r_1}{r_2}=\dfrac{1}{10}~~~~~\textup{[taking square root on both sides]}\\\\\\\Rightarrow r_1:r_2=1:10.

Thus, the required similarity ratio is 1 : 10.

goldfiish [28.3K]3 years ago
6 0
<span>2π m2 and 200π m2

so ratio is 1:100</span>
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Step-by-step explanation:

see the attached figure to better understand the problem

we know that

A <u><em>centroid</em></u> of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.

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Part a) Find ML

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HL=45\ units

we know that

ML=\frac{1}{3}HL

substitute the given value

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HL=45\ units

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substitute the given value

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Part c) Find JM

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JI=63\ units

we know that

JM=\frac{1}{3}JI

substitute the given value

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Part d) Find MI

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we know that

MI=\frac{2}{3}JI

substitute the given value

MI=\frac{2}{3}(63)

MI=42\ units

Part e) Find GM

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KG=60\ units

we know that

GM=\frac{2}{3}KG

substitute the given value

GM=\frac{2}{3}(60)

GM=40\ units

Part f) Find MK

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KG=60\ units

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MK=\frac{1}{3}KG

substitute the given value

MK=\frac{1}{3}(60)

MK=20\ units

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