 Important for :
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

 ⇔ x2 = 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.