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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. EC = 8.1 cm. DC = 5.4 cm. DB = 2.6 cm. (a) Work out the length of AE. AC = 6.15 cm. (b) Work out the leng... 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 AE.

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Answer

To find the length of AE, we can use the property of similar triangles since E.A is parallel to D.B.

Using the ratio of the sides, we have:

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

Plugging in the values:

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

Calculating the right side:

$\frac{2.6}{5.4} = 0.481$

Thus, we have:

$AE = 8.1 \times 0.481 = 3.9 \text{ cm}$

Step 2

(b) Work out the length of AB.

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Answer

To find the length of AB, we can again apply the property of similar triangles:

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

Putting in the known measurements:

$\frac{AB}{6.15} = \frac{8.1}{2.6}$

Calculating the right side:

$\frac{8.1}{2.6} \approx 3.115$

Therefore:

$AB = 6.15 \times 3.115 \approx 19.217 \text{ cm}$

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