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Question
In the given figure, Δ AHK ∼ Δ ABC. If AK = 8 cm, BC = 3.2 cm and HK = 6.4 cm, then find the length of AC.
Solution
ΔAHK ∼ ΔABC (The triangles are similar, which means corresponding sides are proportional.)
AK = 8 cm
BC = 3.2 cm
HK = 6.4 cm
We need to find the length of the AC.
Using the proportionality of the corresponding sides of similar triangles, we have:
`(AC)/(AK)` = `(BC)/(HK)`
Substituting the given lengths:
`(AC)/8` = `3.2/6.4`
This simplifies to:
`(AC)/8 = 1/2`
Therefore:
AC = `8×1/2`
AC = 4 cm
Thus, the length of AC in the triangle is 4 cm.
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