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Answers
16. The length and breadth of a rectangle are 2x + 3y and x - y respectively. Find its perimeter.
→ Length of the rectangle = (2x + 3y) units
Breadth of the rectangle = (x - y) units
We know,
Perimeter of the rectangle = 2(Length + Breadth) units.
Hence,
Perimeter of the rectangle = 2{(2x + 3y) + (x - y)}
Perimeter = 2{2x + 3y + x - y}
Perimeter = 2{3x + y}
Perimeter = 6x + 2y
Hence, Option (c) 6x + 2y is the correct answer.
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17. What must be added to 3x + 4y to get 2x + 3y.
→ To get what must be added to 3x + 4y to get 2x + 3y we must subtract 3x + 4y from 2x + 3y
Hence,
(2x + 3y) - (3x + 4y)
= 2x + 3y - 3x - 4y
= - x - y
Hence, Option (c) - x - y is the correct answer.
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18. What must be subtracted from 3a² - 5ab + 2b² - 1 to get 3a² - 5ab - 3b² - 2
→ Let the required expression be p
ATQ,
p subtracted from 3a² - 5ab + 2b² - 1 will given 3a² - 5ab - 3b² - 2
Hence,
(3a² - 5ab + 2b² - 1) - p = 3a² - 5ab - 3b² - 2
=> -p = (3a² - 5ab - 3b² - 2) - (3a² - 5ab + 2b² - 1)
=> -p = 3a² - 5ab - 3b² - 2 - 3a² + 5ab - 2b² + 1
=> -p = 3a² - 3a² - 5ab + 5ab - 3b² - 2b² - 2 + 1
=> -p = -5b² - 1
=> p = -(-5b² - 1)
=> p = 5b² + 1
Hence, Option (b) 5b² + 1 is the correct answer.
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19. Two adjacent sides of a rectangle are x² + y² and x² + 2xy respectively. Find the perimeter of the rectangle.
→ Length of the rectangle = x² + y²
Breadth of the rectangle = x² + 2xy
We know,
Perimeter of a rectangle = 2(Length + Breadth) units.
Hence,
Perimeter of the rectangle = 2{(x² + y²) + (x² + 2xy)}
Perimeter = 2{x² + y² + x² + 2xy}
Perimeter = 2{2x² + y² + 2xy}
Perimeter = 4x² + 2y² + 4xy
Hence, Option (d) 4x² + 2y² + 4xy is correct answer.
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20. If the three sides of the triangle are given by x + y, x - z, x - y respectively, then find its perimeter.
→ 1st side of triangle = x + y
2nd side of triangle = x - z
3rd side of triangle = x - y
We know,
Perimeter of triangle = 1st side + 2nd side + 3rd side
Hence,
Perimeter = (x + y) + (x - z) + (x - y)
Perimeter = x + y + x - z + x - y
Perimeter = 3x - z
Hence, Option (b) 3x - z is the correct answer.
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21. The perimeter of a triangle is 6x² - 3y + 5 and two of its sides are x² - 2y + 3 and 2x² + 3y - 2. Find the third side the triangle.
→ 1st side = x² - 2y + 3
2nd side = 2x² + 3y - 2
Perimeter = 6x² - 3y + 5
We know,
Perimeter of triangle = 1st side + 2nd side + 3rd side
Hence,
6x² - 3y + 5 = (x² - 2y + 3) + (2x² + 3y - 2) + 3rd side
=> 6x² - 3y + 5 = x² - 2y + 3 + 2x² + 3y - 2 + 3rd side
=> 6x² - 3y + 5 = 3x² + y + 1 + 3rd side
=> (6x² - 3y + 5) - (3x² + y + 1) = 3rd side
=> 6x² - 3y + 5 - 3x² - y - 1 = 3rd side
=> 3x² - 4y + 4 = 3rd side
=> 3rd side = 3x² - 4y + 4
Hence, Option (b) 3x² - 4y + 4 is the correct answer.
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