Luluse se 15 For example. Sam calculated that a 35 mm x 33 mm rectangle has an

area of 1155 mm², whereas rounding 35 mm and 33 mm to the nearest

10 millimetres results in an approximate area of 40 x 30 = 1200 mm.

a A rectangle has length 47 mm and width which is larger than 20 mm

but rounds to 20 mm. The approximate area is larger than the actual

area. Find all possible widths of the rectangle.

To her surprise, Sam found a rectangle whose sides were not a multiple

of 10 millimetres but its actual area was the same as its approximate

area. She decided to call such a rectangle quirky.

b Explain why one side length of a quirky rectangle must round up and

the other side length must round down.

c Explain why one side length of any quirky rectangle is a multiple of

4 mm and the other is a multiple of 25 mm.

d Find the dimensions of all quirky rectangles with side lengths under

100 mm.