# In the given figure, ∆AHK is similar to ∆ABC. If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find AC.

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.

$\frac{\mathrm{AC}}{\mathrm{AK}}=\frac{\mathrm{BC}}{\mathrm{HK}}$

$\frac{\mathrm{AC}}{10}=\frac{3.5}{7}$

$\mathrm{AC}=5 \mathrm{~cm}$