The perimeter of an isosceles triangle is 32 cm. If the base of the triangle is increased by 25%

| April 2, 2021 | education

The perimeter of an isosceles triangle is 32 cm. If the base of the triangle is increased by 25%, and the sides are reduced by 20%, then we get a triangle whose perimeter is 29.2 cm. Find the length of the base on the side of the triangle.

Let the perimeter of the triangle be P = x + 2y, where x is the base, y is the side.

By the condition of the problem 1.25x + (2y – 0.2 * 2y) = 29.2 → 1.25x + 1.4y = 29.2.

Let’s compose a system of equations with two variables:

{x + 2y = 32,

{1.25x + 1.4y = 29.2. From the first equation, we express x through y and substitute it into the second equation:

x = 32 – 2y; 1.25 * (32 – 2y) + 1.4y = 29.2 → 40 – 2.5y + 1.4y = 29.2 → 1.1y = 10.8 → y = 10.8 / 1.1 = 108/11 = 9 9/11. x = 32 – 2 * 108/11 = (352 – 216) / 11 = 136/11 = 12 4/11.

Answer: the length of the base of the triangle is 12 4/11, the sides are 9 9/11.



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