Question

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

• A. 7 cm
• B. 14 cm
• C. 5 cm
• D. 10 cm

Answer 1

The correct option is C 5 cm

Given: ∆AHK ~ ∆ABC, AK = 10 cm,
BC = 3.5 cm, and HK = 7 cm.
AC = ?
Since, ∆AHK ~ ∆ABC,
$\frac{AH}{AB}=\frac{HK}{BC}=\frac{KA}{CA}$ (side ratio)
$\frac{AH}{AB}=\frac{7}{3.5}=\frac{10}{CA}=2$

$\frac{10}{CA}=2$

$\frac{10}{2}=CA$

$CA=5$ cm