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suter [353]
3 years ago
8

The outer and inner triangles are both equilateral and the circle touches all three sides of the outer triangle. If the area of

the inner triangle is 10 square centimeters, what is the area of the outer triangle

Mathematics
1 answer:
Brrunno [24]3 years ago
5 0

Answer:

The area of outer Δ = 40 cm²

Step-by-step explanation:

∵ Area of the small triangle = 10 cm²

If we join the center of the circle with the 3 vertices of the inner Δ

These 3 segments are the radii of the circle

Now the inner triangle has 3 isosceles Δ their sides are r , r and s1 with vertex angle 120° ⇒ (360° ÷ 3 = 120°)

Where r is the radius of the circle and s1 is the side of the inner triangle

<em>By using cosine rule</em>

(s1)² = r² + r² - 2r²cos120 = r² + r² - 2r² (-0.5) = r² + r² + r² = 3r²

∴ s1 = r√3

∵ The radius of the circle ⊥ to the side of the outer Δ because the side of the outer Δ is a tangent to the circle

If we join a vertex of the outer Δ with the center of the circle

We will have a right angle triangle of two legs r and half s2 with angle 60° (120° ÷ 2 )between them ⇒ s2 is the side of outer Δ

∴ tan 60° = 1/2 (s2) ÷ r ⇒ √3 = 1/2 (s2) ÷ r = (s2)/2r

∴ s2 = 2r√3

∴ s2 : s1 = 2r√3 ÷ r√3 = 2 : 1

∴ The side of the outer Δ is double the side of the inner Δ

<em>By using similarity ratio</em>

A2/A1 = (s2/s1)² ⇒ A2 and A1 are the areas of outer and inner triangles

∴ A2 : A1 = (2/1)² = 4/1  

∴ A2 = 4 A1

∴ A2 = 4 × 10 = 40 cm²

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4 0
3 years ago
The standard deviation for a set of data is 6.5. The mean is 255. What is the Margin of Error?​
HACTEHA [7]

Answer: The margin of error is 12.74.

Step-by-step explanation:

Since we have given that

Standard deviation = 6.5

Mean = 255

Let 95% level of significance,

So, z value = 1.96

We need to find the "Margin of error":

So, it becomes :

Margin of error = Standard deviation × z-value

Margin of error = 6.5\times 1.96=12.74

Hence, the margin of error is 12.74.

3 0
3 years ago
8. The difference between two numbers is 14. If 1/3of the larger number is subtracted from the smaller number, the
Serjik [45]

Answer:

The values of the 2 numbers whose sum is 13 and difference is 3, are: {8 ; 5}.

Step-by-step explanation:

7 0
3 years ago
Are the two triangles in the image above similar? If so then what is the correct postulate: SSS, SAS, or AA or None
viktelen [127]

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3 0
3 years ago
The midpoint of segment XY is (6, -3). The coordinates of one endpoint are X(-1, 8). Find the coordinates of endpoint Y.
Snezhnost [94]

Answer:

The answer to your question is:    Y = (13, -14)

Step-by-step explanation:

Data

midpoint = mp = (6, -3)

one endpoint = X = (-1, 8)

second endpoint = Y = (x, y)

Formula

Xmp = (x1 + x2) / 2

Ymp = (y1 + y2) / 2

Process

                    x2 = 2xmp - x1

                    y2 = 2ymp - y1

                   x2 = 2(6) - (-1)                     y2 = 2(-3) - 8

                   x2 = 12 + 1                          y2 = -6 - 8

                   x2 = 13                               y2 = - 14

                   Y = (13, -14)

       

                   

4 0
3 years ago
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