1;The lengths of two sides of atrisngle are 12cm and 15cm.between what two measures should the length of the third side fall.
It has to be greater than 12, and shorter than 12+15cm
Greater than 15-12=3, surely?
To determine the possible range of the length of the third side of a triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the given lengths of the two sides are 12cm and 15cm. So, let's calculate the range for the length of the third side.
1. The longest possible length for the third side occurs when the two given sides are stretched to their maximum sum. So, the longest possible length would be 12cm + 15cm = 27cm.
2. On the other hand, the shortest possible length for the third side occurs when the two given sides are compressed to their minimum difference. So, the shortest possible length would be |12cm - 15cm| = 3cm.
Therefore, the length of the third side should fall between 3cm and 27cm (exclusive), since the endpoints are not included in the possible range.
Hence, the range for the length of the third side of the triangle is 3cm < length < 27cm.