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.

Answer 1

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.