1. The perimeter of a triangle in which the lengths ofall of the sides are integ
ID: 3092035 • Letter: 1
Question
1. The perimeter of a triangle in which the lengths ofall of the sides are integers is 21. If the length of one side ofthe triangleis 8, what is the shortest possible length of anotherside of the triangle? 2. If the lengths of two sides of an isosceles triangleare 7 and 15, what is the perimeter of the triangle? 1. The perimeter of a triangle in which the lengths ofall of the sides are integers is 21. If the length of one side ofthe triangleis 8, what is the shortest possible length of anotherside of the triangle? 2. If the lengths of two sides of an isosceles triangleare 7 and 15, what is the perimeter of the triangle?Explanation / Answer
1. The sum of the lengths of two sides of a triangle must begreater than the third side and the difference between two sidesmust be less than the third. (ex. in a 3 4 5 triangle, 3+4 isgreater than 5, 3+5 is greater than 4 and 4+5 is greater than 3....and 5-4 is less than 3, 5-3 is less than 4 and 4-3 is less than5. ) Therefore, if the sum of the three sides is 21 and one side is8, in order to find the smallest side, we need to assume 8 is themedium lenght (because if it was the longest length, it would notfall in the criteris of triangles). Now, we shall use guess andcheck in order to find the other sizes. the smallest size is 3,while the longest size is 10... 8+3 is greater than 10, and8+3+10=21 2. since it is an isosceles triganle, the possiblecombinations can be 7, 7, and 15 or 15, 15, 7....lets try the firstone 7+7 is less than 15, so those sizes are not possible....letstry the second one... 15+15 is greater than 7, 7+15 isgreater than 15...so thesizes are 7, 15, 15 ...add them together for the perimeter and youget 7+15+15 = 37 if you have any doubt, please privatemessage me if you have any doubt, please privatemessage meRelated Questions
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