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 = \(20 \times 12.5 = 250%\)