The diagram shows a rectangle, ABDE, and two congruent triangles, AFE and BCD - Edexcel - GCSE Maths - Question 15 - 2019 - Paper 3

The area of rectangle ABDE can be calculated as:

$$ext{Area}_{ABDE} = AB imes AE = 1 imes AE = AE$$

The total area of triangles AFE and BCD is:

$$ext{Area}_{total} = ext{Area}_{AFE} + ext{Area}_{BCD} = 12AE + 12AE = 24AE$$

Setting the area of the rectangle equal to the total area of the triangles gives us:

$$AE = 24AE$$

From the proportionality given in the question, we know:

$$AB : AE = 1 : 3 \\ \text{thus} \\ AB = \frac{1}{3}AE$$

Now substituting back into our equation, we can rearrange:

$$AE = 24 \times 1/3 \\ = 8 ext{ cm}$$