Question

In measuring the sides of a rectangle errors of 5% and 3% in excess are made . Find the error present in the calculated area.​

Answer 1

Given :

• In measuring the sides of a rectangle errors of 5% and 3% in excess are made .

To find :

• The error present in the calculated area =?

Step-by-step explanation :

Let the length and breadth of the given rectangle be 50 cm and 30 cm respectively.

Then, original area of the given rectangle = 50 × 30

= 1500 sq cm 

Length is taken 3 % in excess  = 50 + (50 × 3)/100

= 50 + 150/100

= 50 + 15/10

= 515/10

= 103/2 cm

Breadth is taken 5 % in excess = 30 + (30 × 5)/100

= 30 + 150/100

= 30 + 15/10

= 300 + 15/10

= 315/10

= 63/2 cm

Now,

New area of rectangle = length x breadth

= 103/2 × 63/2

= 6489/4

= 1,622.25 cm² 

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

= [(1,622.25 - 1500} × 100]/1500

= (122.25 × 100)/1500

= 12225/1500

= 8.15

Therefore, the error percent is 8.15 %