Question

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

(b) In the given figure, $X Y ∣∣ QR$ , $\frac{PQ}{XQ} = \frac{7}{3}$ and $PR = 6.3$ cm. Find the length of YR.

Approach

Given $△ A HK \sim △ A BC$ with $A K = 10$ cm, $BC = 3.5$ cm, and $HK = 7$ cm. By similarity, $\frac{A K}{A C} = \frac{HK}{BC}$ . Substituting gives $\frac{10}{A C} = \frac{7}{3.5} = 2$ , so $A C = 5$ cm.

Step-by-step working

1
Write the similarity ratio: $\frac{A K}{A C} = \frac{HK}{BC}$
1 mark
2
Substitute: $\frac{10}{A C} = \frac{7}{3.5}$
0.5 marks
3
Solve: $A C = \frac{10 \times 3.5}{7} = 5$ cm
0.5 marks

Concepts used

similar trianglesratio of sidesbasic proportionality theoremfind length

Approach

Step-by-step working

Concepts used

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