Question

BASICSALLY FR33 POINTS IF U CAN SOLVE THIS ONE EAY GEOMETRY QUESTION :)

Answer 1

`\sf \boxed{\sf{19 }}\:inches < x < \boxed{\sf67}\: inches`

Explanation:

To find the range of possible lengths for the third side (x) of the triangle, we apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let the two given sides be 24 inches and 43 inches.

The range of possible lengths for the third side (x) can be calculated as follows:

1. The minimum length of the third side (x) occurs when the two given sides are aligned to create the longest possible triangle:

`\sf x > 43 - 24\\\sf x > 19\: inches`

2. The maximum length of the third side (x) occurs when the two given sides are aligned to create the smallest possible triangle:

`\sf x < 43 + 24\\\sf x < 67\: inches`

So, the range of possible lengths for the third side (x) of the triangle is:

`\sf \boxed{\sf{19 }}\:inches < x < \boxed{\sf67}\: inches`