The side AB of triangle ABC is divided at D in the ratio 3:4. DE is parallel to BC and DF is parallel to AC. \(DE=15\) cm and \(DF=16cm\). Find the length of AC in cm.

Explanation: যেহেতু, DE is parallel to BC এবং DF is parallel to AC, DECF একটি parallelogram. \(DF=CE=16\). Moreover, \(\triangle ADE\) and \(\triangle ABC\) are similar triangles. Given D divides AB in ratio 3:4, so \(AD/DB = 3/4\), and \(AB/DB = (AD+DB)/DB = 7/4\). Since \(\triangle ADE\) and \(\triangle ABC\) are similar, \(AB/DB = AC/CE\). Therefore, \(AC/CE = 7/4\). As a result, \(AC=(7/4)\times CE = (7/4)\times16 = 28\).