Question

if marquise uses the 3 - foot and 8 - foot length beams, what is the range of lengths for the third beam that he could use to form a single triangle? question 3 marquise finds another beam 10 feet in length that he splits in half to make a design of a truss with an upright. construct a diagram to scale and label the dimensions. if you are not sure how to proceed, here are some tips you can use as you

Explanation:

Step1: Recall triangle - side length rule

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side, and the difference between the lengths of any two sides must be less than the length of the third side.

Step2: Calculate the sum and difference of the given side - lengths

The two given side - lengths are \(a = 3\) feet and \(b = 8\) feet. The sum \(a + b=3 + 8=11\) feet, and the difference \(|a - b|=|3 - 8| = 5\) feet.

Step3: Determine the range of the third - side length

Let the length of the third side be \(c\). According to the triangle - side length rule, \(5\lt c\lt11\).
The 10 - foot beam is split in half, so its two parts are each 5 feet long. Since \(5\) is not in the range \(5\lt c\lt11\), we only consider the original non - split beams for the third side.

Answer:

The range of the length of the third beam to form a triangle is \(5\lt c\lt11\) feet.