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If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is
- a)6 cm
- b)5 cm
- c)4.5 cm
- d)4 cm
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then i...
To solve this problem, we need to use the given information about the perimeter and area of the rectangle.
1. Understanding the given information:
- Perimeter of the rectangle = 10 cm
- Area of the rectangle = 4 cm²
2. Finding the equations:
- The formula for the perimeter of a rectangle is: P = 2(l + w), where l is the length and w is the width.
- The formula for the area of a rectangle is: A = l * w.
3. Expressing the given information in equations:
- P = 10 cm
- A = 4 cm²
4. Solving the equations:
- From the perimeter equation, we can express the width as w = (P/2) - l.
- Substituting this value of w in the area equation, we get: A = l * [(P/2) - l].
- Simplifying the equation, we have: 4 = l * (10/2 - l).
- Further simplifying, we get: 4 = l * (5 - l).
5. Solving the quadratic equation:
- Expanding the equation, we have: 4 = 5l - l².
- Rearranging the terms, we get: l² - 5l + 4 = 0.
- Factoring the quadratic equation, we have: (l - 4)(l - 1) = 0.
- Therefore, l = 4 or l = 1.
6. Finding the length:
- Since the length cannot be 1 cm (as it would make the width negative), the length must be 4 cm.
Therefore, the correct answer is option D: 4 cm.
1. Understanding the given information:
- Perimeter of the rectangle = 10 cm
- Area of the rectangle = 4 cm²
2. Finding the equations:
- The formula for the perimeter of a rectangle is: P = 2(l + w), where l is the length and w is the width.
- The formula for the area of a rectangle is: A = l * w.
3. Expressing the given information in equations:
- P = 10 cm
- A = 4 cm²
4. Solving the equations:
- From the perimeter equation, we can express the width as w = (P/2) - l.
- Substituting this value of w in the area equation, we get: A = l * [(P/2) - l].
- Simplifying the equation, we have: 4 = l * (10/2 - l).
- Further simplifying, we get: 4 = l * (5 - l).
5. Solving the quadratic equation:
- Expanding the equation, we have: 4 = 5l - l².
- Rearranging the terms, we get: l² - 5l + 4 = 0.
- Factoring the quadratic equation, we have: (l - 4)(l - 1) = 0.
- Therefore, l = 4 or l = 1.
6. Finding the length:
- Since the length cannot be 1 cm (as it would make the width negative), the length must be 4 cm.
Therefore, the correct answer is option D: 4 cm.
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Community Answer
If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then i...
Perimeter of rectangle = 10 cm
Area of rectangle = 4 cm2
Formula used:
Perimeter of rectangle = 2(l + b)
Area of rectangle = l × b
Where, l = length and b = breadth
Area of rectangle = 4 cm2
Formula used:
Perimeter of rectangle = 2(l + b)
Area of rectangle = l × b
Where, l = length and b = breadth
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If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length isa)6 cmb)5 cmc)4.5 cmd)4 cmCorrect answer is option 'D'. Can you explain this answer?
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