shortest side -- x
medium side -- x+3
longest side -- x+3 + 11 = x + 14
solve x + x+3 + x+14 = 59
medium side -- x+3
longest side -- x+3 + 11 = x + 14
solve x + x+3 + x+14 = 59
medium:17
longest:28
Let the length of the shortest side be "x" inches. The medium side would then be "x + 3" inches, as indicated. And to top it off, the longest side would be "x + 3 + 11" inches. Are you keeping up with the clown math so far?
Now, let's add all the sides together to find the perimeter: x + (x + 3) + (x + 3 + 11) = 59.
Simplifying the equation, we have 3x + 17 = 59. Subtract 17 from both sides, and we get 3x = 42. Divide both sides by 3, and we're left with x = 14.
So, the shortest side is 14 inches. The medium side is x + 3 = 14 + 3 = 17 inches. And the longest side is x + 3 + 11 = 14 + 3 + 11 = 28 inches.
Voila! We've unmasked the lengths of this challenging triangle.
According to the problem statement, the medium side is 3 inches more than the shortest side. So, we can represent the medium side as "x + 3".
The longest side is 11 inches longer than the medium side. Therefore, the longest side can be represented as "(x + 3) + 11".
Now, let's calculate the perimeter of the triangle by adding up the lengths of all three sides:
Perimeter = Shortest side + Medium side + Longest side
Given that the perimeter is 59 inches, we can write the equation:
59 = x + (x + 3) + (x + 3 + 11)
Now, simplify the equation:
59 = x + x + 3 + x + 14
Combine like terms:
59 = 3x + 17
Next, solve for "x":
59 - 17 = 3x
42 = 3x
x = 42 / 3
x = 14
So, the length of the shortest side is 14 inches.
Now, let's find the lengths of the other two sides:
Medium side = x + 3 = 14 + 3 = 17 inches
Longest side = (x + 3) + 11 = 17 + 11 = 28 inches
Hence, the lengths of the sides of the triangle are:
Shortest side: 14 inches
Medium side: 17 inches
Longest side: 28 inches