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# The lengths of a rectangle have been measured to the nearest tenth of a centimetre they are 87.3cm and 51.8cm what is the upper bound for the area and the lower bound for the perimeter?

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Answered Jun 20Maths

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Seyed NasrollahiAn enthusiast Physics and Maths tutor with 5 years of teaching experience.1 students helped

Since the measurements are to the tenth, the error for each is 0.05 cm. When adding numbers, the errors simply add up, so for the perimeter: Value: 2 x ( 87.3 + 51.8) = 278.2 Error: 2 x (0.05 + 0.05) = 0.2 So the lower bound for the perimeter is 278.2 - 0.2 = 278.0 cm When multiplying numbers, you need to find the error as a percentage of the value and add them together. Error in length: 0.05 / 87.3 = 0.057% Error in width: 0.05 / 51.8 = 0.097% Total error percentage: 0.057 + 0.097 = 0.15% Value: 87.3 x 51.8 = 4522.1 Final Error: 0.15% x 4523.14 = 6.8 So the upper bound for the area is 4522.1 + 6.8 = 4528.9