Exercise 16B
Page-194
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 ABCD be a rhombus.Let AC and BD be the diagonals of the rhombus intersecting at a point O.AC=16 cm BD=12 cmWe know that the diagonals of a rhombus bisect each other at right angles.∴ AO=12AC =(12×16) cm =8 cmBO=12BD =(12×12) cm =6 cmFrom the right ∆AOB:AB2=AO2+BO2 ={(8)2+(6)2} cm2 =(64+36) cm2 =100 cm2⇒AB=√100 cm =10 cmHence, the length of the side AB is10 cm.Therefore, the length of each side of the rhombus is 10 cm because all the sides of a rhombus are equal.
Q3 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms
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) 32We know that the sum of adjacent angles of a parallelogram is180°.⇒2x+25+3x-5=180⇒5x+20=180⇒5x=180-20⇒5x=160⇒x=1605⇒x=32Therefore, the value of x is 32.
Q4 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms
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) parallelogramIn a parallelogram, the diagonals do not necessarily intersect at right angles.
Q5 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms
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 ABCD be a rectangle and let the diagonal AC be 25 cm, length AB be 4x cm and breadth BC be 3x cm.Each angle of a rectangle is a right angle.∴∠ABC=90°From the right ∆ABC:AC2=AB2+BC2⇒(25)2=(4x)2+(3x)2⇒625=16x2+9x2⇒625=25x2
x2= 62525=25⇒x=5∴ Length =4×5=20 cmBreadth=3×5=15 cm
∴ P
=70 cm
Q6 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms
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
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+(23×x)=180⇒x+2x3=180⇒(x+2x3)=180⇒5x3=180⇒x=(180×35)⇒x=108Hence, 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
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) rectangle 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
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) 8All the sides of a square are equal.∴AB=BC⇒2x+3=3x-5⇒3+5=3x-2x⇒8=xTherefore, the value of x is 8.
Q10 | Ex-16B | Class 8 | RS AGGARWAL | chapter 16 | Parallelograms
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.The sum of adjacent angles of a parallelogram is 180°.∴ x+2x-24=180⇒3x-24=180⇒3x= 180+24⇒3x=204⇒x=2043⇒x=68∴ Smallest angle=68°Largest angle = (180-68)°=112°
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