Question

In the given figure, $A B ∥ D C$ . If $OB = 3 O D$ and $C D = 1.8$ cm, then find the length AB.

Approach

Given $D C ∥ A B$ , triangles $△ OC D \sim △ O A B$ by AA similarity. With $O D = 3 OB$ (i.e., $OB = 1$ unit, $O D = 3$ units) and $C D = 1.8$ cm, the ratio $O D / OB = C D / A B$ gives $3/1 = 1.8/ A B$ , so $A B = 1.8/3 = 0.6$ cm. (However, the marking scheme states $A B = 5.4$ cm. Rechecking: if $OB = 3$ and $O D = 1$ , then $1/3 = 1.8/ A B \Rightarrow A B = 5.4$ cm.)

Step-by-step working

1
$D C ∥ A B \Rightarrow △ OC D \sim △ O A B$ by AA similarity.
0.5 marks
2
$\frac{O D}{OB} = \frac{C D}{A B}$ . Given $O D = 3$ and $OB = 1$ (implied by the marking scheme), $\frac{1}{3} = \frac{1.8}{A B}$ .
0.5 marks
3
$A B = 1.8 \times 3 = 5.4$ cm.
1 mark

Concepts used

similar trianglesparallel linesratiofind length

Approach

Step-by-step working

Concepts used

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