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Luden [163]
3 years ago
15

The floor of the gazebo shown is a regular octagon. Each side of the floor is 8 feet, and the area is about 309 square feet. You

build a small model gazebo in the shape of a regular octagon. The perimeter of the floor of the model gazebo is 7 feet. Find the area of the floor of the model gazebo to the nearest hundredth of a square foot. What is the ratio of the perimeters (in feet) of the real gazebo floor to the model gazebo floor?
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
8 0

Answer:

Area: 3.7 ft²

Ratio: 73.14 : 1

Step-by-step explanation:

Perimeter of an octagon = 8*side

Replacing with perimeter = 7 ft:

7 = 8*side

side = 7/8 ft = 0.875 ft

that is, each side of the model is 7/8 ft length.

Area of an octagon = 2*(1 + √2)*side²

Area of an octagon = 2*(1 + √2)*(7/8)²

Area of an octagon = 3.7 ft²

Perimeter of real gazebo = 8*8 = 64 ft

Then, the ratio of the perimeters (in feet) of the real gazebo floor to the model gazebo floor is 64:0.875. Multiplying each term by 8/7, we get 73.14:1

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EastWind [94]

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Step-by-step explanation:

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2 years ago
Suppose KLMN ~ PQRS. Find the value of x.
arlik [135]

Complete question is attached.

Answer:

B) 8

Step-by-step explanation:

In this question, KLMN ~ PQRS. This means they are similar shapes.

From the image, we could denote that:

KL ~ PQ

LM ~ QR

Given that:

KL = 12

PQ = 30

QR = 20

LM = x

To find x, let's use tge expression:

\frac{KL}{PQ} = \frac{LM}{QR}

=  \frac{12}{30} = \frac{x}{20}

Cross multiplying, we have:

12 * 20 = 30x

240 = 30x

To find x, let's divide both sides by 30.

\frac{240}{30} = \frac{30x}{30}

8 = x

x = 8

The correct option is option B.

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3 years ago
PLEASE HELP NEED ASAP WILL MARK THE BRAINLIEST
harkovskaia [24]

Answer:

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Step-by-step explanation:

idk

7 0
3 years ago
Help help pls pls!!!!
DIA [1.3K]
What grade are you in?
3 0
2 years ago
How do I solve for x
Alchen [17]
Greetings!

To find the length of any side of a right triangle, you can use the Pythagorean Thereom. It states that the squares of two sides are equal to the square of the hypotenuse:
a^2+b^2=c^2

Input the information from the diagram into the formula: 
(x)^2+(x+7)^2=(13)^2

Expand each term:
(x)^2+(x+7)^2=(13)^2

x^2+((x+7)(x+7))=169

x^2+(x(x+7)+7(x+7))=169

x^2+x^2+7x+7x+49=169

Combine like terms:
2x^2+14x+49=169

Add -169 to both sides:
(2x^2+14x+49)+(-169)=(169)+(-169)

2x^2+14x-120=0

Factor out the Common Term (2):
2(x^2+7x-60)=0

Factor the Complex Trinomial:
2(x^2-5x+12x-60)=0

2(x(x-5)+12(x-5))=0

2(x-5)(x+12)=0

Set Factors to equal 0:
x-5=0

x=5

or

x+12=0

x=-12

However, since we are solving for the side length, the only possible answer is 5 (a shape can't have a side with a negative length.)

The Solution Is: 
\boxed{x=5}

I hope this helped!
-Benjamin

6 0
2 years ago
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