In triangle XYZ, the length of side XY is 26 mm and the length of side YZ is 38 mm. Which of the following could be the length of side XZ?A.44 mmB.69 mmC.10 mmD.66 mm

Accepted Solution

The correct option is:  A. 44 mmExplanationIf the lengths of two given sides of a triangle are [tex]a[/tex] and [tex]b[/tex] , then the possible range for the length of the third side[tex](c)[/tex] will be.....[tex]|a-b|<c<|a+b|[/tex]Here two sides are given as 26 mm and 38 mm. That means, [tex]a= 26[/tex] and [tex]b= 38[/tex]So, [tex]|a-b|=|26-38|=|-12|= 12[/tex]and [tex]|a+b|=|26+38|=|64|=64[/tex]That means the length of the third side must be greater than 12 mm but less than 64 mm. Among the given options, 44 mm is the only option which is greater than 12 but less than 64. So, the length of side XZ could be  44 mm.