14. rooms a rectangular room is 12½ feet wide and 14 feet long. what is the perimeter of the room?
15. cycling the tire for a 10-speed bicycle has a diameter of 27 inches. find the distance traveled in 10 rotations of the tire. round to the nearest tenth.
16. geography earth’s circumference is approximately 25,000 miles. if you could dig a tunnel to the center of the earth, how long would the tunnel be? round to the nearest tenth mile.
find the perimeter of each figure. round to the nearest tenth.
17. image of a composite figure: rectangle with a triangle, dimensions 2.4 cm, 3.5 cm, 2.0 cm
18. image of a shape with two semicircles and a rectangle, dimensions 3 in., 3 in.
19. image of a semicircle, diameter 4 ft
20. image of a semicircle and a right triangle, dimensions 4 m, 3 m, 5 m

Question

Accepted Answer

### Question 14
# Explanation:
## Step1: Recall perimeter formula for rectangle
The perimeter $ P $ of a rectangle is given by $ P = 2\times (length + width) $. Here, the width $ w = 12\frac{1}{2}=\frac{25}{2} $ feet and the length $ l = 14 $ feet.
## Step2: Substitute values into the formula
First, calculate $ length + width $: $ 14+\frac{25}{2}=\frac{28 + 25}{2}=\frac{53}{2} $. Then, multiply by 2: $ P = 2\times\frac{53}{2}=53 $ feet.
# Answer:
The perimeter of the room is 53 feet.

### Question 15
# Explanation:
## Step1: Recall circumference formula for circle
The circumference $ C $ of a circle is $ C=\pi d $, where $ d $ is the diameter. Here, $ d = 27 $ inches.
## Step2: Calculate distance for 10 rotations
First, find the circumference of one rotation: $ C=\pi\times27\approx 84.823 $ inches. Then, for 10 rotations, the distance $ D = 10\times C=10\times84.823 = 848.23 \approx 848.2 $ inches.
# Answer:
The distance traveled in 10 rotations is approximately 848.2 inches.

### Question 16
# Explanation:
## Step1: Recall relationship between circumference and radius
The circumference $ C $ of a circle is $ C = 2\pi r $, where $ r $ is the radius (distance from center to surface). We need to find $ r $ when $ C = 25000 $ miles.
## Step2: Solve for radius
From $ C = 2\pi r $, we get $ r=\frac{C}{2\pi} $. Substitute $ C = 25000 $: $ r=\frac{25000}{2\pi}=\frac{12500}{\pi}\approx 3978.9 $ miles.
# Answer:
The length of the tunnel (radius) is approximately 3978.9 miles.

### Question 17
# Explanation:
## Step1: Identify the figure components
The figure is a rectangle with a triangle attached. The rectangle has length 3.5 cm, width 2.4 cm. The triangle has two sides of 2.0 cm (isosceles triangle with base equal to the width of the rectangle, 2.4 cm? Wait, no, looking at the diagram, the rectangle has length 3.5, width 2.4, and the triangle has two equal sides of 2.0 cm. Wait, actually, the perimeter will be: two lengths of the rectangle, one width, the other width is replaced by the two sides of the triangle? Wait, no, let's see: the figure has a rectangle (with right angles) and a triangle. So the perimeter is: 3.5 (bottom) + 2.4 (left) + 3.5 (top) + 2.0 (right - triangle side) + 2.0 (other right - triangle side). Wait, no, the vertical side on the right is the triangle. Wait, the rectangle has length 3.5, width 2.4. The triangle is attached to the right side of the rectangle. So the perimeter is: 3.5 (bottom) + 2.4 (left) + 3.5 (top) + 2.0 (hypotenuse of triangle) + 2.0 (other hypotenuse? Wait, no, the triangle is isosceles with two sides 2.0 cm and base equal to the width of the rectangle (2.4 cm)? Wait, maybe the perimeter is calculated as: length of rectangle (3.5) + width (2.4) + length (3.5) + two sides of the triangle (2.0 each). Wait, let's add them: $ 3.5+2.4 + 3.5+2.0+2.0=13.4 $ cm? Wait, no, maybe I misread. Wait, the rectangle has length 3.5, width 2.4. The triangle is attached to the right end, so the right side of the rectangle is replaced by the triangle. So the perimeter is: bottom (3.5) + left (2.4) + top (3.5) + two sides of the triangle (2.0 each). So $ 3.5 + 2.4+3.5 + 2.0+2.0 = 13.4 $ cm. Wait, but let's check again. Alternatively, maybe the triangle's base is 2.4 cm (same as the width of the rectangle) and the two equal sides are 2.0 cm. Then the perimeter would be: 3.5 (bottom) + 2.4 (left) + 3.5 (top) + 2.0 (right - triangle side) + 2.0 (other right - triangle side). Yes, that's correct. So sum: $ 3.5+2.4 = 5.9 $, $ 5.9+3.5 = 9.4 $, $ 9.4+2.0 = 11.4 $, $ 11.4+2.0 = 13.4 $ cm.
# Answer:
The perimeter of the figure is 13.4 cm.

### Question 18
# Explanation:
## Step1: Identify the figure components
The figure is a rectangle with two semicircles (which make a full circle) on the ends. The rectangle has length 3 in, and the diameter of the semicircles is 3 in (so radius $ r=\frac{3}{2} $ in).
## Step2: Calculate perimeter
The perimeter is the sum of the two lengths of the rectangle and the circumference of the full circle (from the two semicircles). The circumference of the circle is $ C=\pi d=\pi\times3\approx 9.4248 $ in. The two lengths of the rectangle are $ 3\times2 = 6 $ in. So total perimeter $ P=6 + 9.4248\approx 15.4 $ in (rounded to the nearest tenth).
# Answer:
The perimeter of the figure is approximately 15.4 inches.

### Question 19
# Explanation:
## Step1: Recall perimeter formula for a semicircle
The perimeter of a semicircle is the sum of the half - circumference and the diameter. The formula is $ P=\frac{1}{2}\times\pi d + d $, where $ d $ is the diameter. Here, $ d = 4 $ ft.
## Step2: Substitute values and calculate
First, calculate the half - circumference: $ \frac{1}{2}\times\pi\times4 = 2\pi\approx 6.2832 $ ft. Then add the diameter: $ P=6.2832 + 4=10.2832\approx 10.3 $ ft (rounded to the nearest tenth).
# Answer:
The perimeter of the semicircle is approximately 10.3 feet.

### Question 20
# Explanation:
## Step1: Identify the figure components
The figure is a combination of a semicircle and a right triangle. The semicircle has a radius $ r = 4 $ m (so diameter $ d = 8 $ m), and the triangle has sides 3 m, 4 m, and 5 m (right triangle, 3 - 4 - 5).
## Step2: Calculate perimeter
The perimeter is the sum of the length of the semicircle, the side of the triangle (5 m), and the side of the triangle (3 m). The length of the semicircle is $ \frac{1}{2}\times\pi\times d=\frac{1}{2}\times\pi\times8 = 4\pi\approx 12.5664 $ m. Then add the two sides of the triangle: $ 12.5664+5 + 3=20.5664\approx 20.6 $ m (rounded to the nearest tenth).
# Answer:
The perimeter of the figure is approximately 20.6 meters.

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QUESTION IMAGE

Question

Explanation:

Question 14

Step1: Recall perimeter formula for rectangle

Step2: Substitute values into the formula

Step1: Recall circumference formula for circle

Step2: Calculate distance for 10 rotations

Step1: Recall relationship between circumference and radius

Step2: Solve for radius

Answer:

Question 15