One side of triangle is 4 4 times the shortest side. the third side is 23 23 feet more than the shortest side. the perimeter is 77 77 . find all three sides.

9, 32 and 36

Step-by-step explanation:

The perimeter of a triangle is the sum of all the sides.  Since you know the perimeter and the expressions for each of the sides, you can set up an equation to solve for the variable and find the values of the other sides:

one side: '4 times the shortest side' = 4s

shortest side: 's'

third side: '23 more than the shortest side' = s + 23

perimeter  = 77

Equation:  4s + s + (s + 23) = 77

Combine like terms:  6s + 23 = 77

Subtract 23 from both sides:  6s + 23 - 23 = 77 - 23 or 6s = 54

Divide by 6:  6s/6 = 54/6 or s = 9

one side: 4s = 4(9) = 36

shortest side: s = 9

third side: s + 23 = 9 + 23 = 32