ABC and EDC are straight lines - Edexcel - GCSE Maths - Question 5 - 2017 - Paper 2

To find the length of AB, we can use the segments given.

First, we note that:

$AC = AE + EB$

Since we know AC and AE, we can express EB as:

$EB = AC - AE$

Substituting the known values:

$EB = 6.15 - 3.9 = 2.25$

Now, we relate it back to the total segment AB through the similar triangles property:

$\frac{AB}{AC} = \frac{DB}{EB}$

where DB = 2.6 cm and EB = 2.25 cm. Thus, we can express AB as:

$AB = AC \times \frac{DB}{EB}$

Substituting the values:

$AB = 6.15 \times \frac{2.6}{2.25} \approx 6.15 \times 1.15556 \approx 7.1$

Therefore, the length of AB is approximately 7.1 cm.