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zvonat [6]
3 years ago
8

A circle is inscribed in a square. The area of the circle is 507 square inches. What is the length of each side of the square? U

se 3 for pi.
Mathematics
1 answer:
Lena [83]3 years ago
6 0

Answer:

26 inches

Step-by-step explanation:

We are given;

  • An inscribed circle whose area is 407 square inches
  • In this case, we need to know that an inscribed in a square touches the four sides of the triangle.
  • Therefore, the diameter of the circle is equivalent to the side of the square.

We are given the area as 507 square inches

But;

Area of the circle = pi × r²

Thus we can get the radius of the circle;

Thus;

507 in² = 3 × r²

r² = (507 ÷ 3)

   = 169

r =√169

  = 13 inches

But, Diameter = 2 r

Thus; Diameter = 2 × 13

                        = 26 inches

But, in this case, diameter = side of the square

Therefore, the side of the square is 26 inches

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is

y

−

(

−

3

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2

(

x

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3

)

y

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3

=

3

2

(

x

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⇒

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y

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⇒

3

x

−

2

y

−

15

=

0

Note:

The equn.of line passing through  

A

(

x

1

,

y

1

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and

with slope

m

is

y

−

y

1

=

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(

x

−

x

1

)3

x

−

2

y

−

15

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0

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We know that,

the slope of the line  

a

x

+

b

y

+

c

=

0

is  

m

=

−

a

b

∴

The slope of the line  

2

x

+

3

y

=

9

is  

m

1

=

−

2

3

∴

The slope of the line perpendicular to  

2

x

+

3

y

=

9

is  

m

2

=

−

1

m

1

=

−

1

−

2

3

=

3

2

.

Hence,the equn.of line passing through  

(

3

,

−

3

)

and

m

2

=

3

2

is

y

−

(

−

3

)

=

3

2

(

x

−

3

)

y

+

3

=

3

2

(

x

−

3

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2

y

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6

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x

−

9

⇒

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x

−

2

y

−

15

=

0

Note:

The equn.of line passing through  

A

(

x

1

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and

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3

y

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3

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x

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is the partial equation

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,

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)

into the partial equation

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b

⇒

b

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2

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y

=

3

2

x

−

15

2

←

equation of perpendicular lineExplanation:

the equation of a line in  

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

rearrange  

2

x

+

3

y

=

9

into this form

⇒

3

y

=

−

2

x

+

9

⇒

y

=

−

2

3

x

+

3

←

in slope-intercept form

with slope m  

=

−

2

3

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∙

x

m

perpendicular

=

−

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m

⇒

m

perpendicular

=

−

1

−

2

3

=

3

2

⇒

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)

into the partial equation

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3

=

9

2

+

b

⇒

b

=

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6

2

−

9

2

=

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⇒

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=

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