Mensuration
- The length and breadth of a rectangular field are in the ratio of 3 : 2. If the perimeter of the field is 80m, its breadth (in metres) is :
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Using Rule 9,
Let length be 3x and breadth be 2x
∴ Perimeter = 2 (length + breadth)
= 2(3x + 2x) = 10x
According to question, 10x = 80m
⇒ x = 8m
∴ Breadth = 2x = 2× 8 = 16 mCorrect Option: B
Using Rule 9,
Let length be 3x and breadth be 2x
∴ Perimeter = 2 (length + breadth)
= 2(3x + 2x) = 10x
According to question, 10x = 80m
⇒ x = 8m
∴ Breadth = 2x = 2× 8 = 16 m
- The sides of a rectangular plot are in the ratio 5:4 and its area is equal to 500 sq.m. The perimeter of the plot is :
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Using Rule 9,
Area of rectangle = l × b
∴ 5x × 4x = 500 sq.m.
or, 20x² = 500 sq.m.⇒ x² = 500 = 25 20
⇒ x = 5
∴ l = 5 × 5 = 25 m
⇒ = 5 × 4 = 20 m
∴ Perimeter = 2 (l + b)m
= 2 (25 + 20) = 2 × 45 = 90 mCorrect Option: C
Using Rule 9,
Area of rectangle = l × b
∴ 5x × 4x = 500 sq.m.
or, 20x² = 500 sq.m.⇒ x² = 500 = 25 20
⇒ x = 5
∴ l = 5 × 5 = 25 m
⇒ = 5 × 4 = 20 m
∴ Perimeter = 2 (l + b)m
= 2 (25 + 20) = 2 × 45 = 90 m
- The perimeter of the top of a rectangular table is 28m., whereas its area is 48m². What is the length of its diagonal?
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Using Rule 9,
Let the length = l m and breadth = b m.
∴ 2 (l + b) = 28
⇒ l + b = 14 ... (i)
l b = 48 ....(ii)
Now, (l – b)² = (l + b)² – 4lb
= (14)² – 4 × 48 [From (i) & (ii)]
= 196 – 192 = 4
⇒ l – b = 2 ....(iii)
∴ l = 8, b = 6
∴ Diagonal = √8² + 6² = 10 m.Correct Option: B
Using Rule 9,
Let the length = l m and breadth = b m.
∴ 2 (l + b) = 28
⇒ l + b = 14 ... (i)
l b = 48 ....(ii)
Now, (l – b)² = (l + b)² – 4lb
= (14)² – 4 × 48 [From (i) & (ii)]
= 196 – 192 = 4
⇒ l – b = 2 ....(iii)
∴ l = 8, b = 6
∴ Diagonal = √8² + 6² = 10 m.
- The difference between the circumference and diameter of a circle is 150 m. The radius of that circle is (Take π = 22/7)
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Using Rule 14,
Circumference of circle = π × diameter = πd
∴ πd – d = 150
⇒ d (π – 1) = 150⇒ d 
22 - 1 
= 150 7 ⇒ d 22 - 7 = 150 7 ⇒ d × 15 = 150 7 ⇒ d × 150 × 7 = 70 15 ∴ Radius = d = 70 2 2
= 35 metreCorrect Option: B
Using Rule 14,
Circumference of circle = π × diameter = πd
∴ πd – d = 150
⇒ d (π – 1) = 150⇒ d 22 - 1 = 150 7 ⇒ d 22 - 7 = 150 7 ⇒ d × 15 = 150 7 ⇒ d × 150 × 7 = 70 15 ∴ Radius = d = 70 2 2
= 35 metre
- A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is (Take π = 22/7)
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Using Rule 14,
2πr = 2 (18 + 26)⇒ 2 × 22 × r = 44 × 2 7
⇒ r = 14 cm
∴ Area of circle = πr²= 22 × 14 × 14 = 616 sq. cm. 7 Correct Option: D
Using Rule 14,
2πr = 2 (18 + 26)⇒ 2 × 22 × r = 44 × 2 7
⇒ r = 14 cm
∴ Area of circle = πr²= 22 × 14 × 14 = 616 sq. cm. 7
