Question

1 сторона трикутника у 3 рази менша від другої і на 23 см менша від третьої. Знайдіть стонони трикутника, якщо периметр = 128 см

Answer 1

Problem Analysis

We are given that one side of a triangle is three times smaller than the second side and 23 cm smaller than the third side. We need to find the lengths of the sides of the triangle, given that the perimeter is 128 cm.

Solution

Let's assume the lengths of the sides of the triangle are a, b, and c, with a being the smallest side.

According to the given information, we have the following equations: 1. b = 3a (one side is three times smaller than the second side) 2. c = a + 23 (one side is 23 cm smaller than the third side) 3. a + b + c = 128 (perimeter of the triangle is 128 cm)

We can substitute the values of b and c from equations 1 and 2 into equation 3 to solve for a.

Substituting b = 3a and c = a + 23 into a + b + c = 128, we get: a + 3a + (a + 23) = 128 5a + 23 = 128 5a = 128 - 23 5a = 105 a = 105 / 5 a = 21

Now that we have the value of a, we can substitute it back into equations 1 and 2 to find the values of b and c.

Using b = 3a, we get: b = 3 * 21 b = 63

Using c = a + 23, we get: c = 21 + 23 c = 44

Therefore, the lengths of the sides of the triangle are: a = 21 cm b = 63 cm c = 44 cm

Answer

The lengths of the sides of the triangle are 21 cm, 63 cm, and 44 cm.