The lengths of the sides of a triangle are 3, 5, 7. find the length of the sides of a similar triangle, the perimeter which is 37.5.

Let x be the coefficient of proportionality, then the sides of a triangle, similar to the given triangle by the condition, are equal to 3x, 5x and 7x. The perimeter of a polygon is the sum of the lengths of all its sides. The perimeter of such a triangle is: 3x + 5x + 7x = 37.5; 15x = 37.5; x = 37.5 / 15 (the main property of the “cross to cross” proportion); x = 2.5. Then the length: – the first side of a similar triangle is 3x = 3 * 2.5 = 7.5; – the second side of such a triangle is 5x = 5 * 2.5 = 12.5; – the third side of such a triangle is 7x = 7 * 2.5 = 17.5.
Answer: 7.5; 12.5; 17.5.