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

Question 5

ABC and EDC are straight lines. E A is parallel to D B. E C = 8.1 cm. D C = 5.4 cm. D B = 2.6 cm. (a) Work out the length of A E. A C = 6.15 cm. (b) Work out the... show full transcript

Worked Solution & Example Answer:ABC and EDC are straight lines - Edexcel - GCSE Maths - Question 5 - 2017 - Paper 2

Step 1

(a) Work out the length of A E.

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Answer

To find the length of AE, we use the concept of similar triangles. Since EA is parallel to DB, triangles AEC and DBC are similar. The sides are proportional:

$\frac{AE}{EC} = \frac{DB}{DC}$

Given that:

EC = 8.1 cm
DC = 5.4 cm
DB = 2.6 cm

Substituting the values into the proportion gives:

$\frac{AE}{8.1} = \frac{2.6}{5.4}$

Cross-multiplying to solve for AE:

$AE = 8.1 \times \frac{2.6}{5.4}$

Calculating:

$AE \approx 8.1 \times 0.4815 \approx 3.9 \text{ cm}$

Step 2

(b) Work out the length of A B.

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Answer

To find the length of AB, we again utilizes the similarity of triangles AEC and DBC. We already found AE in part (a), which is approximately 3.9 cm.

Using the same proportion, we have:

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

Given:

AC = 6.15 cm
DB = 2.6 cm
DC = 5.4 cm

Substituting into the proportion:

$\frac{AB}{6.15} = \frac{2.6}{5.4}$

Cross-multiplying gives:

$AB = 6.15 \times \frac{2.6}{5.4}$

Calculating:

$AB \approx 6.15 \times 0.4815 \approx 2.96 \text{ cm}$

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