In the given figure, ∆ AHK ~ ∆ ABC. If AK = 8 cm, BC = 3.2 cm

Q) In the given figure, ∆ AHK ~ ∆ ABC. If AK = 8 cm, BC = 3.2 cm and HK = 6.4 cm, then find the length of AC.

Ans:

Step 1: Since Δ AHK ~ Δ ABC (given)

Therefore, $\frac{HK}{BC} = \frac{AK}{AC}$

∴ AC = $\frac{AK \times BC}{HK}$

Step 2: It is given that AK = 8 cm, BC = 3.2 cm, HK = 6.4 cm

by substituting the given values, we get:

AC = $\frac{8 \times 3.2}{6.4}$

= $\frac{8 \times 1}{2}$

= 4 cm

Therefore, the length of AC is 4 cm

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