A4 The areas of two similar triangles are in the ratio 4 : 9. One of the sides of the smaller triangle measures $6 \mathrm{~cm}$. The corresponding side of the larger triangle measures:
(A) $9 \mathrm{~cm}$
(B) $13.5 \mathrm{~cm}$
(C) $4 \mathrm{~cm}$
(D) $12 \mathrm{~cm}$
(E) none of the above
A4. From the ratio of the areas of similar triangles, $S_{1}: S_{2}=4: 9$, we understand the ratio of corresponding sides of these two triangles $a_{1}: a_{2}=2: 3$. We consider the length of the side of the smaller triangle and use it in the proportion $6: a_{2}=2: 3$. Solve the proportion $2 \cdot a_{2}=6 \cdot 3$. Express $a_{2}=\frac{6 \cdot 3}{2}=9$. The side of the triangle is $9 \mathrm{~cm}$ long.