Question

The length and width of a rectangle are measured as 36 cm and 28 cm, respectively. with an error in measurement of at most 0.2 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.

Answer 1

To estimate the maximum error in the calculated area of the rectangle, we use the differential formula. The maximum error in the area is 12.8 square centimeters.

Step-by-step explanation:

To estimate the maximum error in the calculated area of the rectangle, we need to find the differential of the area formula. The area of a rectangle is given by the formula A = Length imes Width. So, using differentials, we have dA = (dL imes W) + (L imes dW), where dL and dW are the errors in the measurements of length and width respectively.

Given that the length L = 36 cm and dL = 0.2 cm, and width W = 28 cm and dW = 0.2 cm, we can substitute these values into the differential formula to find dA. dA = (0.2 cm imes 28 cm) + (36 cm imes 0.2 cm) = 5.6 cm2 + 7.2 cm2 = 12.8 cm2.

Therefore, the maximum error in the calculated area of the rectangle is 12.8 square centimeters.