The perimeter of the scalene triangle is 60 cm. The length of the longest side is 4 times that of the shortest side.Which statements about the possible measures of the sides are reasonable? Check all that apply.The value of x can equal 40.The longest side can equal 30 cm.The shortest side can equal 7 cm.The value of x can equal 25.The shortest side can equal 5. ​

Accepted Solution

Step-by-step answer:Given:A trianglePerimeter  = 60 cmlongest side = 4* shortest side (x)Solution:longest side = 4xshortest side = xthird (intermediate side = 60 -x -4x = 60-5xThe triangle inequality specifies that the sum of the two shorter sides must be greater than the longest side to form a triangle.  Hencex + y > 4xx + 60-5x > 4x60 - 4x > 4x8x < 60x < 60/8 = 7.5, or x < 7.5Therefore to form a triangle, x (shortest side) must be less than 7.5 cm.Examine the options: both 7 and 5 are both less than 7.5 cm.40, 30 and 25 all have a problem because the longest side (4 times longer) will exceed the perimeter of 60.Now also examine cases where 4x is NOT the longest side, in which case we need4x>=yor4x >= 60-5x9x >=60x >= 6.67so x=5 will not qualify, because 4x will no longer be the longest side.The only valid option is x=7 cmThe side lengths for x=7 and x=5 are, respectively,(7, 25, 28)5, 20, 35  (in which case, the longest side is no longer 4x=20, so eliminated)