Mensuration
- The length of two sides of an isosceles triangle are 15 and 22 respectively. What are the possible values of perimeter ?
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Perimeter of isosceles triangle = 15 + 15 + 22 or 15 + 22 + 22
= 52 or 59 unitsCorrect Option: A
Perimeter of isosceles triangle = 15 + 15 + 22 or 15 + 22 + 22
= 52 or 59 units
- If the length and the perimeter of a rectangle are in the ratio 5 : 16, then its length and breadth will be in the ratio
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Using Rule 9,
Let the length of the rectangle be x units and breadth be y units.
∴ Perimeter of rectangle = 2 (x + y) cm
According to the question,x = 5 2x + 2y 16 ⇒ x = 5 x + y 8 ⇒ x + y = 8 ⇒ y = 8 - 1 x x 5 x 5 ⇒ y = 3 x : y = 5 : 3 x 5 Correct Option: D
Using Rule 9,
Let the length of the rectangle be x units and breadth be y units.
∴ Perimeter of rectangle = 2 (x + y) cm
According to the question,x = 5 2x + 2y 16 ⇒ x = 5 x + y 8 ⇒ x + y = 8 ⇒ y = 8 - 1 x x 5 x 5 ⇒ y = 3 x : y = 5 : 3 x 5
- If the length of each median of an equilateral triangle is 6√3 cm, the perimeter of the triangle is
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If AB = x cm, thenBC = x cm 2
∴ From ∆ABD AB² = BD² + AD²⇒ x² = x² + (6√3)² 4 ⇒ x² = x² = 36 × 3 4 ⇒ 3x² = 36 × 3 4
⇒ x² = 36 × 4
⇒ x = 6 × 2 = 12 cm
∴ Perimeter of equilateral triangle = 3 × 12 = 36 cmCorrect Option: C
If AB = x cm, thenBC = x cm 2
∴ From ∆ABD AB² = BD² + AD²⇒ x² = x² + (6√3)² 4 ⇒ x² = x² = 36 × 3 4 ⇒ 3x² = 36 × 3 4
⇒ x² = 36 × 4
⇒ x = 6 × 2 = 12 cm
∴ Perimeter of equilateral triangle = 3 × 12 = 36 cm
- The sides of a triangle are in the ratio 1/4 : 1/6 : 1/8 and its perimeter is 91 cm. The difference of the length of longest side and that of shortest side is
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Ratio of the sides of triangle = 1 : 1 : 1 4 6 8 = 1 × 24 : 1 × 24 : 1 × 24 4 6 8
[LCM of 4, 6, 8 = 24]
= 6 : 4 : 3
∴ 6x + 4x + 3x = 91
∴ 13x = 91⇒ x = 91 = 7 13
∴ Required difference = 6x – 3x = 3x
= 3 × 7 = 21 cmCorrect Option: D
Ratio of the sides of triangle = 1 : 1 : 1 4 6 8 = 1 × 24 : 1 × 24 : 1 × 24 4 6 8
[LCM of 4, 6, 8 = 24]
= 6 : 4 : 3
∴ 6x + 4x + 3x = 91
∴ 13x = 91⇒ x = 91 = 7 13
∴ Required difference = 6x – 3x = 3x
= 3 × 7 = 21 cm
- The diagonals of a rhombus are 32 cm and 24 cm respectively. The perimeter of the rhombus is:
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Using Rule 12,
We know that rhombus is parallelogram whose all four sides are equal and its diagonals bisect each other at 90°.
∴ AB = √(16)² + (12)⊃
= √256 + 144 = √400
= 20 cm = side of the rhombus
∴ Perimeter of the rhombus = 20 × 4 = 80 cmCorrect Option: A
Using Rule 12,
We know that rhombus is parallelogram whose all four sides are equal and its diagonals bisect each other at 90°.
∴ AB = √(16)² + (12)⊃
= √256 + 144 = √400
= 20 cm = side of the rhombus
∴ Perimeter of the rhombus = 20 × 4 = 80 cm
