Question

(a) In the given figure, $Δ A HK \sim Δ A BC$ . If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find the length of AC.

Approach

In the figure, $△ A HK \sim △ A BC$ by AA similarity. Given $A K = 10$ cm, $BC = 3.5$ cm, $HK = 7$ cm, use the proportion $\frac{A K}{A C} = \frac{HK}{BC} \Rightarrow \frac{10}{A C} = \frac{7}{3.5} = 2 \Rightarrow A C = 5$ cm.

Step-by-step working

1
$△ A HK \sim △ A BC \Rightarrow \frac{A K}{A C} = \frac{HK}{BC}$ .
1 mark
2
$\frac{10}{A C} = \frac{7}{3.5} \Rightarrow A C = 5$ cm.
0.5 marks
3
Therefore, length of $A C = 5$ cm.
0.5 marks

Concepts used

similar trianglesratio of sidesfind lengthproportionality

Approach

Step-by-step working

Concepts used

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