Finding a side from the perimeter

A rectangle is twenty-three centimetres long and its perimeter is seventy-four centimetres. Find its breadth. Try it first. Pause if you like. Perimeter equals length plus breadth plus length plus breadth. Perimeter is the distance all the way round. Follow one length, one breadth, the other length and the other breadth. We know the length. Does it occur once or twice on the way round? There are two equal lengths. Each is twenty-three centimetres, so subtract twenty-three twice. Two times breadth equals seventy-four centimetres minus twenty-three centimetres minus twenty-three centimetres, which equals twenty-eight centimetres. The twenty-eight centimetres is shared by two equal breadths. One breadth is half of it. Breadth of the rectangle equals twenty-eight centimetres divided by two, which equals fourteen centimetres. The breadth of the rectangle is fourteen centimetres. Both lengths came off first. The amount left was two breadths, so we divided by two.

Siti bends a wire sixty-eight centimetres long to form a rectangle nineteen centimetres long. Find the area of the rectangle. Try it first. Pause if you like. Perimeter equals length plus breadth plus length plus breadth. The wire goes all the way round, so it is the perimeter. The two equal lengths are each nineteen centimetres. Both must be subtracted from the wire length. Two times breadth equals sixty-eight centimetres minus nineteen centimetres minus nineteen centimetres, which equals thirty centimetres. Breadth of the rectangle equals thirty centimetres divided by two, which equals fifteen centimetres. We have found the breadth. The question asks for area. Which two dimensions do we multiply? Area of the rectangle equals nineteen centimetres times fifteen centimetres, which equals two hundred and eighty-five square centimetres. The area of the rectangle is two hundred and eighty-five square centimetres. The wire length and the breadth are measured in centimetres. The area inside is measured in square centimetres. Subtract both lengths, then halve the two breadths. For area, multiply length by breadth.