Quadrilateral and parallelogram Questions and answers

Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

Elementary Mathematics

21). If in a parallelogram ABCD, bisectors of consecutive angles A and B intersect at P, then \( \Large \angle APB \) is equal to

A). \( \Large 30 ^{\circ} \)

B). \( \Large 45 ^{\circ} \)

C). \( \Large 60 ^{\circ} \)

D). \( \Large 90 ^{\circ} \)

View Answer

Correct Answer: \( \Large 90 ^{\circ} \)

Since ABCD is a parallelogram,

\( \Large \therefore \angle A + \angle B = 180 ^{\circ} \)

=> \( \Large \frac{1}{2} \angle A + \frac{1}{2}B = 90 ^{\circ} \)

=> \( \Large \angle PAB + \angle PBA = 90 ^{\circ} \)

From \( \Large \triangle ABP, \angle APB = 90 ^{\circ} \)

22). The area of the shaded portion is

A). 8 sq. cm

B). 6 sq. cm

C). 16 sq. cm

D). 4 sq. cm

View Answer

23). Match List-I with List-II and select the correct answer using the codes given below the lists List-I
A. Opposite sides equal and parallel
B. Opposite sides equal and one angle \( \Large 90 ^{\circ} \)
C. All sides equal and each angle \( \Large 90 ^{\circ} \)
D. All sides equal and diagonals at right angles
List-II
1. Rectangle
2. Square
3. Rhombus
4. Parallelogram
Codes:
A B C D

A). 4 1 3 2

B). 3 4 2 1

C). 4 1 2 3

D). 2 4 1 3

View Answer

24). The area of a rectangle and a square are equal. The side of the square is 5 cm and smaller side of the rectangle is half that of the square. The length of other side of the rectangle would be

A). 5 cm

B). 8 cm

C). 10 cm

D). 12.5 cm

View Answer

Correct Answer: 10 cm

Side of square = 5 cm

Area of square = \( \Large 5^{2} \) = 25 sq. cm 5

Width of rectangle = \( \Large \frac{5}{2} \) = 2.5 cm

Let x cm be the length of the other side of rectangle.

Therefore, Area of rectangle = 2.5x sq. cm

=> 2.5x = 25

=> \( \Large x = \frac{25}{2.5} = 10\ cm \)

25). The perimeter of a square is 12 cm and that of another is 16 cm. The side of a square whose area is equal to sum of the areas of the above two squares would be

A). 4 cm

B). 5 cm

C). 5.5 cm

D). 6 cm

View Answer

Correct Answer: 5 cm

Perimeter of first square = 12

Therefore, Its side = \( \Large \frac{12}{4} \) = 3 cm

and its area = \( \Large 3^{2} \) = 9 sq. cm

Perimeter of second square = 16 cm

Therefore, Its side = \( \Large \frac{16}{4} \) = 4 cm

and its area = \( \Large 4^{2} \) = 16 cm

Therefore, Area of new square = 9 + 16 = 25 sq. cm

Therefore, Its side = \( \Large \sqrt{25} \) = 5 cm

26). If perimeter of a rectangle is 48 metres and its area is \( \Large 135 m^{2} \), then sides of the rectangle are

A). 15 m, 9 m

B). 19 m, 5 m

C). 45 m, 3 m

D). 27 m, 5 m

View Answer

Correct Answer: 15 m, 9 m

Let sides of the rectangle are x and y meters

By hypothesis, \( \Large 2 \left(x+y\right)=48 \)

=> \( \Large x+y = 24 \)

=> \( \Large x = 24-y \) ...(i)

and \( \Large xy = 135 \) ...(ii)

From equations (i) and (ii), we get

\( \Large \left(24-y\right)y=135 \)

=> \( \Large 24y-y^{2}=135 \)

=> \( \Large y^{2}-24y+135=0 \)

=> \( \Large y^{2}-15y-9y+135=0 \)

=> \( \Large y \left(y-15\right)-9 \left(y-15\right)=0 \)

=> \( \Large \left(y-15\right) \left(y-9\right)=0 \)

=> y=15, or y=9

From equation (i),

x = 24 - 15 = 9

or x = 24 - 9 = 15

Hence, sides are 15 m, 9 m.

1	2	3

Go to :

Total Pages : 3