7.2. Two isosceles triangles are given, with the same perimeters. The base of the second triangle is $15\%$ larger than the base of the first, and the lateral side of the second triangle is $5\%$ shorter than the lateral side of the first. Find the ratio of the sides of the first triangle.
Answer. The base relates to the lateral side as 2:3. Solution. Let $a$ and $b$ be the length of the base and the lateral side, respectively, of the first triangle. Then its perimeter is $a+2 b$. The base and the lateral side of the second triangle are, respectively, $1.15 a$ and $0.95 b$, and its perimeter is $1.15 a+1.9 b$. Due to the equality of the perimeters, we have $a+2 b=1.15 a+1.9 b$. From this, $0.1 b=0.15 a$. Therefore, $a: b=2: 3$.