Question

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

Answer 1

Answer:

The Length of AC is 5 cm.

Step-by-step explanation:

GIVEN:

∆AHK is similar to ∆ABC

∆AHK ~  ∆ABC

AK = 10cm, BC  = 3.5cm & HK = 7cm

AK/AC = HK/BC  

[corresponding sides of similar triangles are proportional]

10/AC = 7/3.5

10/AC = 7/3.5

7 AC = 10 × 3.5  

7 AC = 35  

AC = 35/7

AC = 5 cm

Hence, the Length of AC is 5 cm.

HOPE THIS ANSWER WILL HELP YOU

Answer 2

Since, triangle ahk is similar to triangle abc(by aa similarity criterion)....

By Thales theorem,

In triangle ahk and triangle abc,

ak/ac=hk/bc (since, the sides of similar triangles are proportional)

10/ac=7/3.5

=> 10/ac= 2

=> ac= 10/5

=> ac=2cm........