In a triangle, the first side is 50% larger than the second, but 25% smaller than the third.

In a triangle, the first side is 50% larger than the second, but 25% smaller than the third. The smaller side was enlarged by 40% and the larger side was enlarged by 25%. How has the perimeter of the triangle changed and by what percentage? response should have increased by 20%

Let the other side be a.
Let the first side be 1.5a.
The first side is 25% smaller than the third.
It is less by 25% not from its length, but from the length of the third, and is:
100% – 25% = 75% or 3/4 the length of the third side. 1.5a = 3/4;

4 / 4a = 1.5: 5 * 4 = 2a;
P₁ = 1.5a + a + 2a = 4.5a;

After changing the lengths of the sides, they became 1.5a.
a * 1.4 = 1.4a;
2a * 1.25 = 2.5a;
P2 = 1.5a + 1.4a + 2.5a = 5.4a
P2 – P1 = 0.9a;

Let’s express it as a percentage:
0.9a: 4.5a * 100 = 20%.