The lower bound for the area of the rectangle is 220,869 mm² (to three significant figures), and the upper bound for the perimeter of the rectangle is 2100 mm.
To calculate the lower bound for the area of the rectangle, we take the smallest possible values of the length and width that would round to the measurements given when rounded to the nearest 5 mm. Since Terry measured the length as 745 mm correct to the nearest 5 mm, the smallest it could actually be is 742.5 mm. The width was measured as 300 mm correct to the nearest 5 mm, so the smallest it could actually be is 297.5 mm. To find the area, we multiply the lower bounds of the length and width.
Area = length × width
Area = 742.5 mm × 297.5 mm
Area = 220,868.75 mm2
The lower bound for the area is 220,868.75 mm2, which is 220,869 mm2 when rounded to three significant figures.
To calculate the upper bound for the perimeter of the rectangle, we consider the largest possible values for the length and width. This would be 747.5 mm for the length and 302.5 mm for the width since we are rounding to the nearest 5 mm. The perimeter is the sum of all sides, so we calculate it by adding twice the length and twice the width.
Perimeter = 2 × length + 2 × width
Perimeter = 2 × 747.5 mm + 2 × 302.5 mm
Perimeter = 2100 mm
The upper bound for the perimeter of the rectangle is 2100 mm.