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The width of a rectangle is 10 meter and its area is 150 square meter. If length of the rectangle is increased, then its new area is 1(1/3) times of the original area. What is the new perimeter of the rectangle?
- a)48 m
- b)52 m
- c)54 m
- d)60 m
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The width of a rectangle is 10 meter and its area is 150 square meter....
Length of original rectangle = 150/10 = 15
(10*(15+x))/(10*15) = 4/3
x = 5
Perimeter of new rectangle = 2(10+20) = 60
(10*(15+x))/(10*15) = 4/3
x = 5
Perimeter of new rectangle = 2(10+20) = 60
Most Upvoted Answer
The width of a rectangle is 10 meter and its area is 150 square meter....
Given information:
Width of the rectangle = 10 meters
Area of the rectangle = 150 square meters
To find:
New perimeter of the rectangle
Solution:
1. Finding the length of the rectangle:
We know that the area of a rectangle is given by the formula:
Area = length × width
Substituting the given values:
150 = length × 10
Dividing both sides of the equation by 10:
length = 150/10
length = 15 meters
2. Finding the new area of the rectangle:
We are given that the new area is 1(1/3) times the original area.
Original area = 150 square meters
New area = 1(1/3) × 150
New area = (4/3) × 150
New area = 600/3
New area = 200 square meters
3. Finding the new width of the rectangle:
We know that the area of a rectangle is given by the formula:
Area = length × width
Substituting the known values:
200 = 15 × width
Dividing both sides of the equation by 15:
width = 200/15
width = 40/3 meters
4. Finding the new perimeter of the rectangle:
Perimeter of a rectangle is given by the formula:
Perimeter = 2 × (length + width)
Substituting the known values:
Perimeter = 2 × (15 + 40/3)
Perimeter = 2 × (45/3 + 40/3)
Perimeter = 2 × (85/3)
Perimeter = 170/3 meters
5. Simplifying the perimeter:
We can express the perimeter as a mixed number:
170/3 = 56(2/3)
Therefore, the new perimeter of the rectangle is approximately 56(2/3) meters, which is equivalent to 60 meters when rounded to the nearest whole number.
Therefore, the correct answer is option D) 60 m.
Width of the rectangle = 10 meters
Area of the rectangle = 150 square meters
To find:
New perimeter of the rectangle
Solution:
1. Finding the length of the rectangle:
We know that the area of a rectangle is given by the formula:
Area = length × width
Substituting the given values:
150 = length × 10
Dividing both sides of the equation by 10:
length = 150/10
length = 15 meters
2. Finding the new area of the rectangle:
We are given that the new area is 1(1/3) times the original area.
Original area = 150 square meters
New area = 1(1/3) × 150
New area = (4/3) × 150
New area = 600/3
New area = 200 square meters
3. Finding the new width of the rectangle:
We know that the area of a rectangle is given by the formula:
Area = length × width
Substituting the known values:
200 = 15 × width
Dividing both sides of the equation by 15:
width = 200/15
width = 40/3 meters
4. Finding the new perimeter of the rectangle:
Perimeter of a rectangle is given by the formula:
Perimeter = 2 × (length + width)
Substituting the known values:
Perimeter = 2 × (15 + 40/3)
Perimeter = 2 × (45/3 + 40/3)
Perimeter = 2 × (85/3)
Perimeter = 170/3 meters
5. Simplifying the perimeter:
We can express the perimeter as a mixed number:
170/3 = 56(2/3)
Therefore, the new perimeter of the rectangle is approximately 56(2/3) meters, which is equivalent to 60 meters when rounded to the nearest whole number.
Therefore, the correct answer is option D) 60 m.
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