The areas of two similar triangles are in the ratio 25 : 49. The perimeter of the larger triangle is 18 cm more than the perimeter of the smaller one.
Find the perimeter of the smaller triangle (in cm).

Perimeters are in the ratio $\sqrt{\frac{25}{49}}=\frac{5}{7}$. Writing them as 5$k$ and 7$k$ gives $7k-5k=2k=18$, so $k=9$ and the smaller perimeter = $5\times 9=45$ cm. The option 63 cm is the larger perimeter; 18.75 uses the area ratio 25 : 49 (a difference of 24 parts) instead of 5 : 7, and 90 cm treats the whole 18 cm as one part.