Type the correct answer in each box. Use numerals instead of words.

An A-frame restaurant is shaped as a triangle with two side lengths of 20 m and 30 m. Complete the inequality below to describe the range of possible lengths [tex]\( x \)[/tex] of the third side of the restaurant.

[tex]\[ \square \ \textless \ x \ \textless \ \square \][/tex]



Answer :

To determine the range of possible lengths [tex]\( x \)[/tex] for the third side of a triangle when the other two sides are known, we need to apply the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Given two side lengths are 20 meters and 30 meters, let's denote these sides as [tex]\( \text{side1} \)[/tex] and [tex]\( \text{side2} \)[/tex] respectively.

1. Determine the lower bound: Calculate the absolute difference between the two known side lengths.
[tex]\[ \text{lower bound} = |30 - 20| = 10 \][/tex]

2. Determine the upper bound: Calculate the sum of the two known side lengths.
[tex]\[ \text{upper bound} = 20 + 30 = 50 \][/tex]

Therefore, the range of possible lengths [tex]\( x \)[/tex] for the third side of the triangle is:
[tex]\[ 10 < x < 50 \][/tex]

So, the completed inequality is:
[tex]\[ 10 < x < 50 \][/tex]