Question

In fig. ∆AHK ~ ∆ABC. If AK = 10cm, BC = 3.5cm and HK = 7cm, find AC.

Answer 1

Two Triangles are said to be similar if their i)corresponding angles are equal and ii)corresponding sides are proportional.(the ratio between the lengths of corresponding sides are equal)

GIVEN:
AK = 10cm, BC  = 3.5cm & HK = 7cm
∆AHK ~  ∆ABC

AK/AC = HK/BC
[corresponding sides of similar triangles are proportional]

10/AC = 7/3.5
10/AC = 70/35
10/AC = 10/5
10AC = 10 × 5
AC = (10 × 5) /10

AC = 5 cm

Hence, the value of AC is 5 cm.

HOPE THIS WILL HELP YOU...

Answer 2

Given that ∆ABC is similar to ∆AKH.

Corresponding sides of similar triangles are proportional to each other.

Therefore,

BCHK= ACAK ⇒(3.5 cm)(7.5 cm) = AC(10 cm)

∴AC = 5 cm