Class 6 Exam > Class 6 Questions > If the area of rectangle increases from 2 cm2...
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If the area of rectangle increases from 2 cm2 to 4 cm2 the perimeter will
- a)decreases
- b)increases
- c)remain same
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If the area of rectangle increases from 2 cm2 to 4 cm2 the perimeter w...
Explanation:
When the area of a rectangle increases, it means that either the length or the width or both have increased. Let us assume that the length and width of the rectangle are l and w respectively.
Given, the initial area of the rectangle is 2 cm² and the final area is 4 cm².
Initial area = length x width = 2 cm²
Final area = length x width = 4 cm²
We can write these equations as:
lw = 2
lw = 4
From these equations, we can see that the length and width of the rectangle have increased. Let us assume that the length and width of the rectangle have increased by x and y respectively.
New length = l + x
New width = w + y
New area = (l + x)(w + y) = lw + ly + wx + xy
We know that lw = 2 and ly + wx + xy = 2
Therefore, New area = 2 + 2 = 4 cm²
Now, let us compare the perimeters of the initial and final rectangle.
Initial perimeter = 2(l + w) = 2(√2) ≈ 2.8 cm
Final perimeter = 2(l + x + w + y) = 2(√6) ≈ 4.9 cm
We can see that the final perimeter is greater than the initial perimeter. Therefore, the correct answer is option (b) increases.
When the area of a rectangle increases, it means that either the length or the width or both have increased. Let us assume that the length and width of the rectangle are l and w respectively.
Given, the initial area of the rectangle is 2 cm² and the final area is 4 cm².
Initial area = length x width = 2 cm²
Final area = length x width = 4 cm²
We can write these equations as:
lw = 2
lw = 4
From these equations, we can see that the length and width of the rectangle have increased. Let us assume that the length and width of the rectangle have increased by x and y respectively.
New length = l + x
New width = w + y
New area = (l + x)(w + y) = lw + ly + wx + xy
We know that lw = 2 and ly + wx + xy = 2
Therefore, New area = 2 + 2 = 4 cm²
Now, let us compare the perimeters of the initial and final rectangle.
Initial perimeter = 2(l + w) = 2(√2) ≈ 2.8 cm
Final perimeter = 2(l + x + w + y) = 2(√6) ≈ 4.9 cm
We can see that the final perimeter is greater than the initial perimeter. Therefore, the correct answer is option (b) increases.
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Community Answer
If the area of rectangle increases from 2 cm2 to 4 cm2 the perimeter w...
If the area of rectangle increases, generally the perimeter will increase.
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