the perimeter of a triangle is 59 inches. the longest side is 11 inches longer than the medium side, and the medium side is 3 inches more than the shortest side. Find the length of each side.
shortest:14
medium:17
longest:28
Ah, the lengths of a triangle! Let's clown around with some variables to help us solve this riddle.
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.
To find the lengths of the sides of the triangle, we'll use algebraic expressions. Let's represent the length of the shortest side as "x".
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
shortest side -- x
medium side -- x+3
longest side -- x+3 + 11 = x + 14
solve x + x+3 + x+14 = 59