A carpenter was told to make a rectangular desk with top of dimension 50cm by 40cm. The carpenter actually made the desk 60cm by 35cm.
(a) Calculate the percentage error in the (i) length and the breadth ; (ii) area of the table top.
(b) Find the product of the two errors in a(i).
Explanation
Error in length = 60cm – 50cm = 10cm
Error in breadth = 40cm – 35cm = 5cm
(i) % error in length = (frac{10}{50} times 100% = 20%)
% error in breadth = (frac{5}{40} times 100% = 12.5%)
(ii) Area of the actual table = (50cm times 40cm = 2000cm^{2})
Area of the table in error = (60cm times 35cm = 2100cm^{2})
Error in area = (2100cm^{2} – 2000cm^{2} = 100cm^{2})
% error in area = (frac{100}{2000} times 100% = 5%)
(b) Product of the error in length and in breadth = (20 times 12.5 = 250%)