We need to work out the upper and lower bounds for each side given: 
87.3
Upper bound : 87.35
Lower bound :87.25

51.8
Upper bound :51.85
Lower bound :51.75

We know the area of a rectangle is width*length so for the upper bound for the area we multiply the upper bound fo width and the upper bound of length together:
So 87.35 * 51.85 = 4529.1cm^2

We know that the perimeter is each side of the rectangle added together, so for the lower bound for the perimeter we add the lower bound of each side:
2* 87.25 + 2* 51.75 = 278.0cm

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


GCSE

Maths

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?

Experienced

Valuable

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

Imperial College London

University of Cambridge

Computer Science

Physics

Seyed Nasrollahi

Profile

Q&A

Seyed Nasrollahi