Question

In the given figure, ΔАНK ~ ΔABC. If AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find the length of AС.

Answer 1

Given ΔАНK ~ ΔABC, the corresponding sides are:

`(AH)/(AB) = (HK)/(BC) = (AK)/(AC)`

From the given data:

AK = 10 cm, BC = 3.5 cm, HK = 7 cm

We use the ratio:

`(HK)/(BC) = (AK)/(AC)`

Substituting the values:

`7/3.5 = 10/(AC)`

Since 3.5 × 2 = 7:

`2 = 10/(AC)`

`AC = 10/2`

AC = 5 cm

The length of AC is 5 cm.