Directions: Study the following questions carefully and choose the right answer.
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.