Missing side length, step by step

Knowing that area is length times width is one thing.

The question
10?A = 50 cm

Missing side: area 50, one side 10

10 × ? =50
× is undone by ÷
50 ÷ 10 =5 cm
check: 10 × 5 =50
  1. Forwards, area is one side times the other: 10 × ? = 50. Every number you need is here, which is exactly why the usual mistake is to multiply them.
  2. But the 50 is the ANSWER to that multiplication, not another side. To get back to the missing one, undo the multiply — and the undo of multiplying is dividing.
  3. 50 ÷ 10 = 5 cm. Check it forwards: 10 × 5 = 50, which is what the question said.

How it works.

  1. 01

    Forwards, area is one side times the other: 10 × ? = 50. Every number you need is here, which is exactly why the usual mistake is to multiply them.

  2. 02

    But the 50 is the ANSWER to that multiplication, not another side. To get back to the missing one, undo the multiply — and the undo of multiplying is dividing.

  3. 03

    50 ÷ 10 = 5 cm. Check it forwards: 10 × 5 = 50, which is what the question said.