Determine if there is a triangle with a perimeter of 47 cm in which one side is 10 cm less

| July 18, 2021 | education

Determine if there is a triangle with a perimeter of 47 cm in which one side is 10 cm less than the other and 5 cm more than the third.

1. Let’s denote one side of the triangle by x cm.

Then, according to the condition of the problem, its second side will be equal to (x – 10) cm, and the third (x + 5) cm.

2. Let’s write down and solve the equation, since we know that the sum of all three sides is 47 cm.

x cm + (x – 10) cm + 9x + 5) cm = 47 cm;

3 x = 47 cm + 10 cm – 5 cm;

3 x = 52 cm, whence x = 52: 3 = 17 1/3 cm.

Determine the length of the second side

x – 10 cm = 17 1/3 cm – 10 cm = 7 1/3 cm.

The value of the third party is calculated as the addition action

x + 5 = 17 1/3 cm + 5 cm = 22 1/3 cm

Let’s check: 17 1/3 + 7 1/3 + 22 1/3 = 47 cm.

Answer: Such a triangle exists.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.