RS Aggarwal Class 8 Math Sixteenth Chapter Parallelograms Exercise 16B Solution
EXERCISE 16B
OBJECTIVE QUESTIONS
Tick (√) the correct answer in each of the following:
(1) The two diagonals are not necessarily equal in a
Ans: (c) Rhombus
(2) The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The length of each side of the rhombus is
Ans: (c) 10 cm
(3) Two adjacent angles of a parallelogram are (2x + 25)o and (3x – 5)o. The value of x is
Ans: (b) 32
∴ (2x + 25) + (3x – 5) = 180
⇒ 2x + 25 + 3x – 5 = 180
⇒ 5x = 180 – 20
⇒ 5x = 160
⇒ x = 32
(4) The diagonals do not necessarily intersect at right angles in a
Ans: (a) Parallelogram.
(5) 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
Ans: (c) 70 cm
Solution: Let the length AB be 4x and Breadth BC be 3x.
Each angle of a rectangle is a right angle. We have,
∴ ∠ABC = 90o
From the right ∆ABC:
AC2 = AB2 + BC2
⇒ (25)2 = (4x)2 + (3x)2
⇒ 16x2 + 9x2 = 625
⇒ 25x2 = 625
⇒ x2 = 25
⇒ x = 5
Therefore, length = 4 × 5 = 20 cm and breadth = 3 × 5 = 15 cm.
(6) The bisectors of any two adjacent angles of a parallelogram intersect at
Ans: (d) 90o
(7) If an angle of a parallelogram is two-thirds of its adjacent angle, the smallest angle of the parallelogram is
Ans: (b) 72o
Solution: Let the measure of the angle be xo.
Hence the one angle is 108o.
Its adjacent = (180 – 108)o = 72o
Therefore, the smallest angle is 72o.
(8) The diagonals do not necessarily bisect the interior angles at the vertices in a
Ans: (a) rectangle
(9) In a square ABCD, AB = (2x + 3) cm and BC = (3x – 5) cm. Then, the value of x is
Ans: (d) 8
Solution: We know, all sides are equal of a square. Then,
∴ AB = BC
⇒ 2x + 3 = 3x – 5
⇒ 3x – 2x = 3 + 5
⇒ x = 8
(10) If one angle of a parallelogram is 24o less than twice the smallest angle then the largest angle of the parallelogram is
Ans: (c) 112o
Solution: Let the measure of smallest angle be xo and other is (2x – 24)o.
∴ x + (2x – 24) = 180
⇒ x + 2x = 180 + 24
⇒ 3x = 204
⇒ x = 68
Hence, the smallest angle is 68o.
Its adjacent is = (180 – 68)o = 112o.
Therefore, the largest angle is 112o.
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