The perimeter of a triangle is 65 in. The longest side is 14 in. longer than the medium side, and the medium side is 6 in. more than the shortest side. Find the length of each side of the triangle.
l = the longest side
m = the medium side
s = the shortest side
The longest side is 14 in longer than the medium side means:
l = m + 14
The medium side is 6 in more than the shortest side means:
m = s + 6
Replace this value in equation:
l = m + 14
l = s + 6 + 14
l = s + 20
The perimeter:
P = s + m + l = 65
s + s + 6 + s + 20 = 65
3 s + 26 = 65
Subtract 26 to both sides
3 s = 39
Divide both sides by 3
s = 13 in
m = s + 6 = 13 + 6 = 19 in
l = s + 20 = 13 + 20 = 33 in
the longest side = 33 in
the medium side = 19 in
the shortest side = 13 in
The perimeter:
P = s + m + l = 13 + 19 + 33 = 65 in
To solve this problem, let's start by assigning variables to the lengths of the sides of the triangle. Let's call the shortest side x inches.
According to the problem, the medium side is 6 inches more than the shortest side. So the medium side would be (x + 6) inches.
The longest side is given as 14 inches longer than the medium side. So the longest side would be (x + 6 + 14) inches, which simplifies to (x + 20) inches.
The perimeter of a triangle is the sum of the lengths of all three sides. So we can set up the following equation:
x + (x + 6) + (x + 20) = 65
Now, let's solve for x:
3x + 26 = 65
Subtracting 26 from both sides:
3x = 39
Dividing both sides by 3:
x = 13
So the shortest side is 13 inches.
Plugging this value back into our expressions for the medium and longest sides, we get:
Medium side = x + 6 = 13 + 6 = 19 inches
Longest side = x + 20 = 13 + 20 = 33 inches
Therefore, the lengths of the sides of the triangle are 13 inches, 19 inches, and 33 inches.