Question

In measuring the sides of a rectangle breadth is taken 5% in excess and the length is taken 4% in deficit find the error percent in the area calculate from the measurements

Answer 1

Solution :-

Let the length and breadth of the given rectangle be 50 cm and 40 cm respectively.

Then, original area of the given rectangle = 50*40

= 2000 sq cm 

Length is taken 4 % in deficit  = 50 - (50*4)/100

= 50 - 2

= 48 cm

Breadth is taken 5 % in excess = 40 + (40*5)/100

= 40 + 2 

42 cm

New area = L*B

= 48*42

= 2016 sq cm 

Error percent in area = (Change in area*100)/Original area

⇒ [(2016 - 2000}*100]/2000

⇒ (16*100)/2000

⇒ 1600/2000

= 0.8 %

So, error percent is 0.8 %

Answer.

Answer 2

Let the length and breadth of a rectangle be 20 cm and 10 cm respectively.

Area without error measurements:

Original Area = length*breadth = 20*10 = 200 sq.cm

Error measurements:

After 5 percent increase of breadth, it becomes 10.5 cm

After 4 percent decrease in length, it becomes 19.2 cm

Area with error measurements:

Increased Area = length*breadth = (10.5)(19.2) = 201.6 sq.cm

Percentage increase in Area = (Change in area*100)/Original area

= [(201.6 - 200)*100]/200

= (1.6*100)/200

= 160/200

= 0.8%

Answer: There is an error of 0.8% increase in area

Hope it helps