Mensuration
- An equilateral triangle is drawn on the diagonal of a square. The ratio of the area of the triangle to that of the square is
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Using Rule 6 and 10,
Let the side of the square be x units, then
diagonal = 2x units
∴ Area of the square = x² and area of triangle= √3 (√2x)² 4 = √ 3x² sq. units 2
∴ Required ratio= x² : √ 3x² = 2 : √ 3 sq. units 2 Correct Option: C
Using Rule 6 and 10,
Let the side of the square be x units, then
diagonal = 2x units
∴ Area of the square = x² and area of triangle= √3 (√2x)² 4 = √ 3x² sq. units 2
∴ Required ratio= x² : √ 3x² = 2 : √ 3 sq. units 2
- A cow is tied on the corner of a rectangular field of size 30 m ×20 m by a 14m long rope. The area of the region, that she can graze,
is (use π = 22/7) :
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Using Rule 17,
Required area = π r² 4 = 22 × 14 × 14 = 154m² 7 × 4 Correct Option: C
Using Rule 17,
Required area = π r² 4 = 22 × 14 × 14 = 154m² 7 × 4
- A circle and a square have equal areas. The ratio of a side of the square and the radius of the circle is
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Using Rule 10 and 14,
Let the radius of circle be r units and the side of square be x units, then
x² = πr²⇒ x² = π ⇒ x = √π or √π : 1 r² 1 r 1 Correct Option: B
Using Rule 10 and 14,
Let the radius of circle be r units and the side of square be x units, then
x² = πr²⇒ x² = π ⇒ x = √π or √π : 1 r² 1 r 1
- If the perimeters of a rectangle and a square are equal and the ratio of two adjacent sides of the rectangle is 1 : 2 then the ratio of area of the rectangle and that of the square is
-
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Using Rule 9 and 10,
Let Side of rectangle are 2x and x units.
and Side of square = y units
∴ 4y = 6x⇒ x = 4 = 2 y 6 3 ∴ 2x × x = 2x² = 2 × 4 y² y² 9
= 8 : 9Correct Option: D
Using Rule 9 and 10,
Let Side of rectangle are 2x and x units.
and Side of square = y units
∴ 4y = 6x⇒ x = 4 = 2 y 6 3 ∴ 2x × x = 2x² = 2 × 4 y² y² 9
= 8 : 9
- Area of regular hexagon with side ‘a’ is
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Using Rule 6,
Area of regular hexagon
6 equilateral triangles= 6 × √3 (side)² 4 = 3√3 a² 2 = 3√3 × √3 a² 2√3 = 9 a² sq.units. 2√3 Correct Option: C
Using Rule 6,
Area of regular hexagon
6 equilateral triangles= 6 × √3 (side)² 4 = 3√3 a² 2 = 3√3 × √3 a² 2√3 = 9 a² sq.units. 2√3
