Mensuration
- A lawn is in the form of a rectangle having its breadth and length respectively in the ratio 2 : 3. The area of the lawn is 600 sq. metres. Find the length of the lawn
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2x × 3x = 600
⇒ 6x² = 600
⇒ x² = 100
⇒ x = 10
∴ Length = 3 × 10 = 30 metreCorrect Option: B
2x × 3x = 600
⇒ 6x² = 600
⇒ x² = 100
⇒ x = 10
∴ Length = 3 × 10 = 30 metre
- The breadth of a rectangular plot is decreased by 20 per cent. By what percent should the length be increased to keep the area same?
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0 = x – 20 – 20x 100 
Net effect = 
x + y + xy 
% 
100 ⇒ x - 20 - x = 0 5
⇒ 5x – 100 – x = 0
⇒ 4x = 100
⇒ x = 25%Correct Option: A
0 = x – 20 – 20x 100 Net effect = x + y + xy % 100 ⇒ x - 20 - x = 0 5
⇒ 5x – 100 – x = 0
⇒ 4x = 100
⇒ x = 25%
- A cow is grazing in a pasture bordered by two fences more than ten feet long that meet at an angle of 60°. If the cow is tethered by a ten foot rope to the post where the fences meet, it can graze an area of:
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Required region = 60° × πr² 360° = 50π sq. feet 3 Correct Option: B
Required region = 60° × πr² 360° = 50π sq. feet 3
- CD is a ⊥ dropped from C. If the area of ∆ADC is ‘a’, then the area of D BDC is :
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5² + 12² = 13²
∆ABC is a right angled triangle.
∆ADC + ∆BDC = ∆ABC⇒ a + ∆BDC = 1 × 5 × 12 = 30 2
⇒ ∆BDC = (30 – a) sq. units.Correct Option: A
5² + 12² = 13²
∆ABC is a right angled triangle.
∆ADC + ∆BDC = ∆ABC⇒ a + ∆BDC = 1 × 5 × 12 = 30 2
⇒ ∆BDC = (30 – a) sq. units.
- The radius of each circle is ‘a’. Then the area of the shaded portion is :
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AB = BC = CA = 2aArea of ∆ABC = √3 × (2a)² 4
= √3a²Area of three sectors = 3 × 60 × πa² = πa² 360 2 ∴ Area of shaded region = √3a² - πa² 2 = a² √3 - π sq.units 2 Correct Option: A
AB = BC = CA = 2aArea of ∆ABC = √3 × (2a)² 4
= √3a²Area of three sectors = 3 × 60 × πa² = πa² 360 2 ∴ Area of shaded region = √3a² - πa² 2 = a² √3 - π sq.units 2
