Question:
In the given figure, ∆AHK is similar to ∆ABC. If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find AC.
Solution:
Given: $\triangle \mathrm{AHK} \sim \triangle \mathrm{ABC}$
AK = 10 cm
BC = 3.5 cm
HK = 7 cm
To find: AC
Since $_{\triangle \mathrm{AHK}} \sim \Delta \mathrm{ABC}$, so their corresponding sides are proportional.
$\frac{\mathrm{AC}}{\mathrm{AK}}=\frac{\mathrm{BC}}{\mathrm{HK}}$
$\frac{\mathrm{AC}}{10}=\frac{3.5}{7}$
$\mathrm{AC}=5 \mathrm{~cm}$
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