Find a side from the perimeter, step by step

A rectangle's perimeter is the two sides doubled, so halving it gives back the length plus the width.

The question
18?P = 50 cm

Missing side: perimeter 50, one side 18

2 × (18 + ?) =50
50 ÷ 2 =25
50 ÷ 2 =25
25 − 18 =7 cm
  1. Forwards, the perimeter goes round twice: 50 is 18 + ? + 18 + ? — each side counted two times.
  2. So undo the doubling FIRST: half of 50 is 25, and that is one long side plus one short one. Taking 18 off the whole 50 is the natural wrong move — it forgets that 18 is in there twice.
  3. Now take the side you know off that half: 25 − 18 = 7 cm.

How it works.

  1. 01

    Forwards, the perimeter goes round twice: 50 is 18 + ? + 18 + ? — each side counted two times.

  2. 02

    So undo the doubling FIRST: half of 50 is 25, and that is one long side plus one short one. Taking 18 off the whole 50 is the natural wrong move — it forgets that 18 is in there twice.

  3. 03

    Now take the side you know off that half: 25 − 18 = 7 cm.