Triangle ABC and triangle DEF are similar - Edexcel - GCSE Maths - Question 5 - 2022 - Paper 3

To find the length of EF, we can use the property of similar triangles, which states that the corresponding sides of similar triangles are in proportion.

First, we determine the ratio of the sides:

the sides of triangle ABC are: AB = 5 cm, BC = 4 cm, AC is unknown.

the sides of triangle DEF are: DE = 22 cm, EF is unknown, DF = 20 cm.

Using the ratios:

$\frac{AB}{DE} = \frac{BC}{EF}$

Substituting the known values:

$\frac{5}{22} = \frac{4}{EF}$

Cross-multiplying gives:

$5 \cdot EF = 4 \cdot 22$

$5 \cdot EF = 88$

Dividing by 5:

$EF = \frac{88}{5} = 17.6 \text{ cm}$