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

To solve for the possible values of $x$, we can use the properties of similar triangles.

Step 1: Setting Up the Proportion

Since triangle ABC is similar to triangle EDC, the ratios of corresponding sides can be set equal:

$\frac{AB}{ED} = \frac{AC}{EC}$

Substituting the given lengths:

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

Step 2: Solving for x

Cross-multiplying gives us:

$8x = 12 \times 3$

Calculating the right side:

$8x = 36$

Now, divide both sides by 8:

$x = \frac{36}{8} = 4.5$

Step 3: Finding the Second Value of x

We also have another pair of corresponding sides:

$\frac{AB}{ED} = \frac{BC}{CD}$

Substituting the lengths:

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

Cross-multiplying again gives us:

$8 \times 12 = 3x$

$96 = 3x$

Dividing both sides by 3:

$x = \frac{96}{3} = 32$

Conclusion

Thus, the two possible values of x are:

1. $x = 4.5$ cm
2. $x = 32$ cm

Assumptions

1. Both triangles are stated to be similar in the problem.
2. The sides listed correspond accurately between the two triangles.