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3 years ago

Two similar polygons have areas of 4 square inches and 64 square inches.

Mathematics

2 answers:

snow_lady [41]3 years ago

4 0

Answer:

Option A is correct

The ratio of a pair of corresponding sides is 1/4

Step-by-step explanation:

Definition:

If two polygons are similar, then

the area of similar figure is the square of the ratio of its corresponding sides.

As per the statement:

Two similar polygons have areas of 4 square inches and 64 square inches

Let the corresponding sides of the polynomials are a and b.

then by definition we have;

$\frac{4}{64}=\frac{a^2}{b^2}$

⇒ $\frac{1}{16} = (\frac{a}{b})^2$

⇒ $\sqrt{\frac{1}{16}} =\frac{a}{b}$

⇒ $\frac{1}{4} = \frac{a}{b}$

$\frac{a}{b} = \frac{1}{4}$

Therefore, The ratio of a pair of corresponding sides is 1/4.

Alex_Xolod [135]3 years ago

3 0

The ratio of a pair of corresponding sides of 1/16.

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<h3>How to determine the orthocenter?</h3>

<u>Question 8</u>

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y = n(x - x1) + y1

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(x1, y1) = (2,0)

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y = 1(x - 2) + 0

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m = (y2 - y1)/(x2 - x1)

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m =(0 - 0)/(6 - 2)

m =0

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n = -1/m

n = undefined

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x = x1

Where:

(x1, y1) = (2,4)

So, we have:

x = 2

Substitute x = 2 in y = x - 2

y = 2 - 2

y = 0

So, we have:

(x, y) = (2, 0)

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<u>Question 9</u>

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A(1,1); B(3, 4); C(6,1)

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m = (y2 - y1)/(x2 - x1)

So, we have:

m =(1 - 4)/(6 - 3)

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n = -1/m

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Where:

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y = 1(x - 1) + 1

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n = -1/m

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This means that the perpendicular line is a vertical line

The equation of the perpendicular line is

x = x1

Where:

(x1, y1) = (3,4)

So, we have:

x = 3

Substitute x = 3 in y = x

y = 3

So, we have:

(x, y) = (3, 3)

Hence, the orthocenter of ABC is (3, 3)

<h3>How to solve for x?</h3>

<u>Question 18 - 20</u>

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