Is there a triangle in which one side is 5 cm less than the second and 2 cm less than the third, the perimeter is 16 cm.

| February 8, 2021 | education

Let’s say such a triangle exists.

Let x denote the length of the smaller side of this triangle.

In the initial data for this task, it is reported that this side is 5 cm less than the second side and 2 cm less than the third, therefore, the length of the second side should be x + 5 cm, and the length of the third side should be x + 2 cm.

Since the sum of the lengths of all three sides of this triangle is 16 cm, we can draw up the following equation:

x + x + 5 + x + 2 = 16,

solving which, we get:

3x + 7 = 16;

3x = 16 – 7;

3x = 9;

x = 9/3 = 3.

Therefore, the lengths of the sides of this triangle are 3 cm, 3 + 5 = 8 cm and 3 + 2 = 5 cm.

Since the sum of the lengths of the first and third sides is less than the length of the second side, such a triangle does not exist.

Answer: There is no such triangle.



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