The two triangles in the diagram are similar - Edexcel - GCSE Maths - Question 22 - 2017 - Paper 1

We can also set up another proportion based on the correspondence of the sides:

$\frac{x}{3} = \frac{8}{12}$

Cross-multiplying again gives us:

$x \cdot 12 = 8 \cdot 3$

This simplifies to:

$12x = 24$

Dividing both sides by 12 gives:

$x = 2$

However, we must consider the relationship between the sides in reverse. Using the sides 8 cm and 3 cm, to find another x:

$\frac{x}{8} = \frac{12}{x}$

Cross-multiplying gives:

$x^2 = 96$

Taking the square root of both sides yields:

$x = 4√{6} \approx 14.7$

1. Both triangles are similar by corresponding angles (AA criterion).
2. The lengths of the sides are directly proportional.