myhelper: RS Aggarwal solution class 8 chapter 16 Parallelograms Exercise 16B

Exercise 16B

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Q1 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

Question 1:

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The two diagonals are not necessarily equal in a
(a) rectangle
(b) square
(c) rhombus
(d) isosceles trapezium

Answer 1:

$(c) rhombus In a rhombus, the two diagonals are not necessarily equal .$

Q2 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

Question 2:

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The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The length of each side of the rhombus is
(a) 8 cm
(b) 9 cm
(c) 10 cm
(d) 12 cm

Answer 2:

$(c) 10 cm$

$Let A B C D be a rhombus . L et A C and B D be the diagonals of the rhombus intersecting at a point O . A C = 16 cm B D = 12 cm We know that the diagonals of a rhombus bisect each other at right angles . ∴ A O = \frac{1}{2} A C = (\frac{1}{2} \times 16) cm = 8 cm B O = \frac{1}{2} B D = (\frac{1}{2} \times 12) cm = 6 cm From the right ∆ A O B : A B^{2} = A O^{2} + B O^{2} = \{{(8)}^{2} + {(6)}^{2}\} {cm}^{2} = (64 + 36) {cm}^{2} = 100 {cm}^{2} \Rightarrow A B = \sqrt{100} cm = 10 cm Hence, the length of the side A B i s 10 cm . Therefore, the length of each side of the rhombus is 10 cm because all t h e sides of a rhombus are equal .$

Q3 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Question 3:

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Two adjacent angles of a parallelogram are (2x + 25)° and (3x − 5)°. The value of x is
(a) 28
(b) 32
(c) 36
(d) 42

Answer 3:

$(b) 32 We know that the sum of adjacent angles of a parallelogram i s 180 ° . \Rightarrow 2 x + 25 + 3 x - 5 = 180 \Rightarrow 5 x + 20 = 180 \Rightarrow 5 x = 180 - 20 \Rightarrow 5 x = 160 \Rightarrow x = \frac{160}{5} \Rightarrow x = 32 Therefore, the value of x is 32 .$

Q4 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Question 4:

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The diagonals do not necessarily intersect at right angles in a
(a) parallelogram
(b) rectangle
(c) rhombus
(d) kite

Answer 4:

$(a) parallelogram In a parallelogram, the diagonals do not necessarily intersect at right angles .$

Q5 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Question 5:

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The length and breadth of a rectangle are in the ratio 4 : 3. If the diagonal measures 25 cm then the perimeter of the rectangle is
(a) 56 cm
(b) 60 cm
(c) 70 cm
(d) 80 cm

Answer 5:

(c) 70 cm

$Let A B C D be a rectangle and let the diagonal A C b e 25 cm, length A B b e 4 x cm and breadth B C b e 3 x cm . Each angle of a rectangle is a right angle . ∴ ∠ A B C = 90 ° From the right ∆ A B C : A C^{2} = A B^{2} + B C^{2} \Rightarrow {(25)}^{2} = {(4 x)}^{2} + {(3 x)}^{2} \Rightarrow 625 = 16 x^{2} + 9 x^{2} \Rightarrow 625 = 25 x^{2}$

$x^{2} = \frac{625}{25} = 25 \Rightarrow x = 5 ∴ L ength = 4 \times 5 = 20 cm Breadth = 3 \times 5 = 15 cm$

∴ Perimeter of the rectangle = 2(20+15) cm
$= 70 c m$

Q6 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Question 6:

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The bisectors of any two adjacent angles of a parallelogram intersect at
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer 6:

$(d) 90 ° The bisectors of any two adjacent angles of a parallelogram intersect at 90 ° .$

Q7 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Question 7:

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If an angle of a parallelogram is two-thirds of its adjacent angle, the smallest angle of the parallelogram is
(a) 54°
(b) 72°
(c) 81°
(d) 108°

Answer 7:

$(b) 72 ° Let x ° be the angle of the parallelogram . Sum of the adjacent angles of a parallelogram is 180 ° . ∴ x + (\frac{2}{3} \times x) = 180 \Rightarrow x + \frac{2 x}{3} = 180 \Rightarrow (x + \frac{2 x}{3}) = 180 \Rightarrow \frac{5 x}{3} = 180 \Rightarrow x = (180 \times \frac{3}{5}) \Rightarrow x = 108 Hence, one angle of the parallelogram is 108 ° . Its adjacent angle = (180 - 108) ° = 72 ° Therefore, the smallest angle of the parallelogram is 72 ° .$

Q8 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Question 8:

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The diagonals do not necessarily bisect the interior angles at the vertices in a
(a) rectangle
(b) square
(c) rhombus
(d) all of these

Answer 8:

$(a) r ectangle In a rectangle, the diagonals do not necessarily bisect the interior angles at the vertices .$

Q9 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Question 9:

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In a square ABCD, AB = (2x + 3) cm and BC = (3x − 5) cm. Then, the value of x is
(a) 4
(b) 5
(c) 6
(d) 8

Answer 9:

$(d) 8 A ll the sides of a square are equal . ∴ A B = B C \Rightarrow 2 x + 3 = 3 x - 5 \Rightarrow 3 + 5 = 3 x - 2 x \Rightarrow 8 = x Therefore, the value of x is 8 .$

Q10 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Question 10:

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If one angle of a parallelogram is 24° less than twice the smallest angle then the largest angle of the parallelogram is
(a) 68°
(b) 102°
(c) 112°
(d) 176°

Answer 10:

$(c) 112 ° Let x ° be the smallest angle of the parallelogram . T he sum of adjacent angles of a parallelogram is 180 ° . ∴ x + 2 x - 24 = 180 \Rightarrow 3 x - 24 = 180 \Rightarrow 3 x = 180 + 24 \Rightarrow 3 x = 204 \Rightarrow x = \frac{204}{3} \Rightarrow x = 68 ∴ Smallest angle = 68 ° L argest angle = (180 - 68) ° = 112 °$

RS Aggarwal solution class 8 chapter 16 Parallelograms Exercise 16B

Exercise 16B

Page-194

Q1 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

Question 1:

Answer 1:

Q2 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

Question 2:

Answer 2:

Q3 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Answer 3:

Q4 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Answer 4:

Q5 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Answer 5:

Q6 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

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Answer 6:

Q7 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

Question 7:

Answer 7:

Q8 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

Question 8:

Answer 8:

Q9 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

Question 9:

Answer 9:

Q10 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms

Question 10:

Answer 10:

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