Directions: Study the following questions carefully and choose the right answer.
Important for :
1
Find the area of a square, one of whose diagonals is 3.8 m long.
» Explain it
A
 Area of the square = 1 × (diagonals)2 2

 ⇒ ( 1 × 3.8 × 3.8 ) m2  ⇒  7.22 m2. 2

Hence, option A is correct.

2
A room 5 m 44 cm long and 3 m 74 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
» Explain it
C
Area of the room

= (544 × 374) cm2 .

Size of the largest square tile

= H.C.F of 544 cm and 374 cm

= 34 cm.

Area of 1 tile = (34 × 34) cm2.

Number of tiles required =

 ( 544 × 374 ) ⇒ 176. 34 × 34

Hence, option C is correct.

3
The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
» Explain it
C
Side of first square =

 ( 40 ) cm ⇒ 10 cm; 4

Side of second square =

 ( 32 ) cm  ⇒ 8 cm. 4

Area of third square

= [(10)2 - (8)2 ] cm2

⇒  (100 - 64) cm2

⇒ 36 cm2.

Side of the third square

 ⇒ 36 cm  ⇒  6 cm.

So, Required perimeter

= (6 × 4) cm ⇒ 24 cm.

Hence, option C is correct.

4
A rectangular grassy plot 110 m by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq. metre.
» Explain it
D
Area of the plot

= (110 × 65) m2

⇒ 7150 m2.

Area of the plot excluding the path

= [(110 – 5) × (65 – 5)] m2

⇒ 6300 m2.

So, area of the path

= (7150 – 6300) m2

⇒  850 m2

Cost of gravelling the path

 = Rs ( 850 × 80 ) ⇒ Rs 680. 100

Hence, option D is correct.

5
The area of rectangle is equal to the area of a circle whose radius is 14 cm. If the breadth of the rectangle is 22 cm, what is its length?
» Explain it
B
Given that,

Area of rectangle = Length x breadth = Area of circle = πr2

 l x b = 22 × 14 × 14 = 616 cm2 7

l x 22 = 616

Therefore, length of the rectangle will be = 28 cm

Hence, option B is correct.