You are trying to determine the area of the floor of a rectangular closet since you will be replacing the carpet. you measure the length to be (5.0±0.1)m and the width to be (3.8±0.1)m. what is the maximum possible area based on the measurements and associated errors? what is the minimum possible area based on the measurements and associated errors?

Explanation:

length L = 5±.1

percentage error

= 0.1/5 x 100 = 2%

breadth b = 3.8 ±.1

percentage error

= .1 / 3.8 x 100

= 2.6 %

Maximum reading of length = 5.1 m

maximum reading of breadth = 3.9m

maximum area possible = 5.1 x 3.9

= 19.9 m².

maximum possible error in the measurement of area in percentage terms

= 2+2.6 = 4.6 %

error in maximum area

19.9 x 4.6 /100

= .9 m²

Minimum possible measurement of area

4.9 x 3.7 = 18.1 m²

possible error

18.1 x 4.6 / 100

= .8 m²

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y