GCSE Edexcel Maths Geometry Toolkit: Triangle ABC and triangle DEF ar

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

Question 5

Triangle ABC and triangle DEF are similar. (a) Work out the length of EF: (b) Work out the length of AB.

Worked Solution & Example Answer:Triangle ABC and triangle DEF are similar - Edexcel - GCSE Maths - Question 5 - 2022 - Paper 3

Step 1

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Answer

Since triangle ABC is similar to triangle DEF, the ratios of corresponding sides are equal. We can set up the proportion:

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

Here, we know the lengths:

To find EF, we use the ratios:

$\frac{4}{20} = \frac{5}{EF}$

Cross-multiplying gives us:

$4 \cdot EF = 5 \cdot 20$

This simplifies to:

$4 \cdot EF = 100$

Dividing both sides by 4 gives:

$EF = \frac{100}{4} = 25 \text{ cm}$

Step 2

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Answer

Using the similarity ratio of sides again:

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

We know:

Setting up the proportion:

$\frac{AB}{20} = \frac{5}{25}$

Cross-multiplying gives:

$AB \cdot 25 = 5 \cdot 20$

Simplifying:

$AB \cdot 25 = 100$

Dividing both sides by 25 gives:

$AB = \frac{100}{25} = 4 \text{ cm}$