∆ABC and ∆PQR are similar. The areas of these two triangles are 289 sq.cm and 576 sq.cm, respectively. If PR = 12 cm, then AC = ?

Correct option is B

Given:
Area of triangle ABC = 289 sq. cm.
Area of triangle PQR = 576 sq. cm.
PR = 12 cm
Formula:
Ratio of area of similar triangles = $$(Ratio \ of \ sides \ of \ triangle)^2$$​​
Solution:

Let the length of side AC be x cm.
PR = 12 cm
According to the question,
Ratio of the area of both triangles = 289 : 576
Putting the values in the formula, we get
​$$\frac{289}{576}=(\frac{x}{12})^2 \\\ \\\frac{x}{12}=√(\frac{289}{576})=\frac{17}{24}\\\ \\x=\frac{17}{24}×12=\frac{17}{2}=8.5 cm$$​​