Mensuration
- If the circumference of a circle is increased by 50% then the area will be increased by
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Using Rule 10,
For an increase of 50% in the circumference of circle, the radius of circle should be increased by 50%.
Then, required percentage increase in the area of the circle= 50 + 50 + 50 × 50 100
= 100 + 25 = 125 %Correct Option: D
Using Rule 10,
For an increase of 50% in the circumference of circle, the radius of circle should be increased by 50%.
Then, required percentage increase in the area of the circle= 50 + 50 + 50 × 50 100
= 100 + 25 = 125 %
- The perimeter of a triangle and an equilateral triangle are same. Also, one of the sides of the rectangle is equal to the side of the triangle. The ratio of the area of the rectangle and the triangleis
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Using Rule 1 and 9,
Let Length of rectangle = x units
and breadth = y units
∴ Side of triangle = y units
⇒ 2x + 2y = 3y
⇒ 2x = y ...(i)∴ Areaof rectangle Area of triangle = xy √3 y² 4 = 4x √3y = 4x = 2 or 2 : √3 √3.2x √3 Correct Option: C
Using Rule 1 and 9,
Let Length of rectangle = x units
and breadth = y units
∴ Side of triangle = y units
⇒ 2x + 2y = 3y
⇒ 2x = y ...(i)∴ Areaof rectangle Area of triangle = xy √3 y² 4 = 4x √3y = 4x = 2 or 2 : √3 √3.2x √3
- Each side of a rectangular field is diminished by 40%. By how much per cent is the area of the field diminished ?
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Using Rule 10,
Let the length and breadth of a rectangle are changed by x% and y% respectively, the effective change in area= 
x + y + xy 
% 100
Here, x = – 40
y = – 40∴ Percentage decrease = -40 - 40 + 40 × 40 % 100
= (– 80 + 16) % = – 64%
Negative sign shows decrease.Correct Option: B
Using Rule 10,
Let the length and breadth of a rectangle are changed by x% and y% respectively, the effective change in area= x + y + xy % 100
Here, x = – 40
y = – 40∴ Percentage decrease = -40 - 40 + 40 × 40 % 100
= (– 80 + 16) % = – 64%
Negative sign shows decrease.
- If each side of a square is increased by 10%. its area will be increased by
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Using Rule 10,
Increase percent in area = 10 + 10 + 10 × 10 % = 21% 100 Correct Option: B
Using Rule 10,
Increase percent in area = 10 + 10 + 10 × 10 % = 21% 100
- If the length of a rectangular plot of land is increased by 5% and the breadth is decreased by 10%, how much will its area increase or decrease ?
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Using Rule 10,
Net % effect = x - y - xy % 100 = 5 - 10 - 5 × 10 % 100
= (–5 – 0.5)% = – 5.5%
The negative sign shows decrease.Correct Option: B
Using Rule 10,
Net % effect = x - y - xy % 100 = 5 - 10 - 5 × 10 % 100
= (–5 – 0.5)% = – 5.5%
The negative sign shows decrease.
