Directions: Study the following questions carefully and choose the right answer.
1
One side of rectangular field is 15 m and one of its diagonals is 17 m find the area of the field?  
» Explain it
B
Other side = (17)2 – (15)2

289 – 225

64 = 8m

So, area = (15 × 8) m2 ⇒ 120 m2.

Hence, option B is correct. 

2
A lawn is in the form of a rectangle having its sides in the ratio 2:3 The area of the lawn is 1/6 hectares. Find the length and breadth of the lawn.
» Explain it
D
 Let length = 2x meters and the breadth = 3x meters.

Now,  area =

  ( 1  × 10000 ) m2
6

( 5000 ) m2
3

So,  2x × 3x   =   5000
3
 
⇔ x= 2500
9

 ⇔ x =  ( 50 ) .
3

So,

Length = 2x =  100   m = 33 1  m
3 3

and

Breadth = 3x =  ( 3 ×  50 )  m = 50 m.
3

Hence, option D is correct.

3
Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs. 12.40 per metre?
» Explain it
A
Area of the carpet  = 

Area of the room =

(13 × 9) m2

⇒ 117 m2.

Length of the carpet =  ( Area )
Width

 ⇒  ( 117 ×  4 )  m ⇒ 156 m.
3

So, Cost of carpeting  = 

Rs. (156 × 12.40)

⇒ Rs. 1934.40.

Hence, option A is correct.

4
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. find the length of the rectangle.
» Explain it
D
Let breadth = x. then, length = 2x. then,

(2x - 5) (x +5) – 2x × x = 75   

⇒  5x – 25 = 75 ⇔ x = 20

So, length of the rectangle = 2x

Therefore,  2 × 20 cm ⇒ 40 cm.


Hence, option D is correct.

5
In measuring the sides of a rectangle, one side is taken 5% in excess, and the other 4% in deficit. Find the error percent in the area calculated from these measurements.
» Explain it
C
Let x and y be the sides of the rectangle. Then, correct area = xy.

Calculated area = 

( 105   x )   ×  ( 96  y )
100 100

⇒  504 xy.
500

Error is measuremant = 

( 504  xy )  = xy +  4 xy.
500 500

So,   Error % =  

[ 4   xy  ×  1   × 100 ] %
500 xy

⇒  4  %  ⇒  0.8%
5

Hence, option C is correct.