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Section C · Triangles Q31

In $\triangle ABC$, $D$ and $E$ are points on sides $AB$ and $AC$ respectively such that $DE \parallel BC$. If $AD = 12$, $DB = 6$ and $AE = 16$, find $EC$, $AB$ and $AC$.

3
ABCDE12 cm6 cm16 cm

Marking scheme

By the Basic Proportionality Theorem, $\dfrac{AD}{DB} = \dfrac{AE}{EC}$ 1
$EC = \dfrac{16 \times 6}{12} = 8$ 1
$AB = AD + DB = 18$ and $AC = AE + EC = 24$ 1
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SecQuestion typeQuestionsMarks
A Multiple Choice Questions 1–18 · 1 each 18
A Assertion and Reason 19–20 · 1 each 2
B Very Short Answer 21–25 · 2 each 10
C Short Answer 26–31 · 3 each 18
D Long Answer 32–35 · 5 each 20
E Case Study Based 36–38 · 4 each 12
Mathematics · full paper · 3 hours 80

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