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A poster is 1.5 m long and 75 cm wide. Which of the following is the ratio (in lowest terms) of the length and perimeter of the poster?
- a)150:450
- b)1:3
- c)150:225
- d)3:1
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A poster is 1.5 m long and 75 cm wide. Which of the following is the r...
**Given Information:**
- Length of the poster = 1.5 m
- Width of the poster = 75 cm
**Finding the Perimeter of the Poster:**
- Perimeter is the sum of all the sides of a shape.
- For a rectangle, the perimeter is calculated by adding the lengths of all four sides.
- In this case, the poster is a rectangle, so the perimeter can be calculated using the formula:
Perimeter = 2 * (Length + Width)
**Converting the Width to Meters:**
- The width of the poster is given in centimeters (cm), but the length is given in meters (m).
- To compare the length and perimeter, we need to convert the width to meters.
- 1 meter = 100 centimeters, so the width in meters = 75 cm / 100 = 0.75 m.
**Calculating the Perimeter:**
- Using the formula, Perimeter = 2 * (Length + Width), we can substitute the values:
Perimeter = 2 * (1.5 m + 0.75 m) = 2 * 2.25 m = 4.5 m
**Calculating the Ratio:**
- To find the ratio of the length to the perimeter, we divide the length by the perimeter.
- Ratio = Length / Perimeter = 1.5 m / 4.5 m = 1/3
**Simplifying the Ratio:**
- The ratio 1/3 can be simplified further by dividing both the numerator and denominator by their greatest common divisor.
- The greatest common divisor of 1 and 3 is 1, so dividing both by 1 gives us:
Simplified Ratio = 1/3
**Conclusion:**
- The ratio of the length to the perimeter of the poster is 1:3, which matches option b) 1:3.
- Length of the poster = 1.5 m
- Width of the poster = 75 cm
**Finding the Perimeter of the Poster:**
- Perimeter is the sum of all the sides of a shape.
- For a rectangle, the perimeter is calculated by adding the lengths of all four sides.
- In this case, the poster is a rectangle, so the perimeter can be calculated using the formula:
Perimeter = 2 * (Length + Width)
**Converting the Width to Meters:**
- The width of the poster is given in centimeters (cm), but the length is given in meters (m).
- To compare the length and perimeter, we need to convert the width to meters.
- 1 meter = 100 centimeters, so the width in meters = 75 cm / 100 = 0.75 m.
**Calculating the Perimeter:**
- Using the formula, Perimeter = 2 * (Length + Width), we can substitute the values:
Perimeter = 2 * (1.5 m + 0.75 m) = 2 * 2.25 m = 4.5 m
**Calculating the Ratio:**
- To find the ratio of the length to the perimeter, we divide the length by the perimeter.
- Ratio = Length / Perimeter = 1.5 m / 4.5 m = 1/3
**Simplifying the Ratio:**
- The ratio 1/3 can be simplified further by dividing both the numerator and denominator by their greatest common divisor.
- The greatest common divisor of 1 and 3 is 1, so dividing both by 1 gives us:
Simplified Ratio = 1/3
**Conclusion:**
- The ratio of the length to the perimeter of the poster is 1:3, which matches option b) 1:3.
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Community Answer
A poster is 1.5 m long and 75 cm wide. Which of the following is the r...
Perimeter= 150*2+75*2 = 450 cm.
length = 1.5m = 150 cm.
length: perimeter= 150:450 = 1:3
length = 1.5m = 150 cm.
length: perimeter= 150:450 = 1:3
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A poster is 1.5 m long and 75 cm wide. Which of the following is the ratio (in lowest terms) of the length and perimeter of the poster?a)150:450b)1:3c)150:225d)3:1Correct answer is option 'B'. Can you explain this answer?
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