The perimeter of a triangle is equal to 12 inches. The length of the longest side is equal to the sum of the other two sides minus 2. If you add 2 to the shortest side, it will equal the longest side. Find the side lengths.
let ..
shortest side ---- x
longest side ---- x+2
middle side ----- y
"The length of the longest side is equal to the sum of the other two sides minus 2"
x+2 = x+y-2
y = 4
x + x+2 + y = 12
2x + 6 = 12
x = 3
sides : 3, 4, and 5
28
Let's denote the lengths of the three sides of the triangle as a, b, and c.
According to the given information, we have the following three equations:
1. The perimeter of the triangle is equal to 12 inches:
a + b + c = 12
2. The length of the longest side (c) is equal to the sum of the other two sides (a and b) minus 2:
c = a + b - 2
3. If you add 2 to the shortest side (a), it will equal the longest side (c):
a + 2 = c
We can now solve these equations simultaneously to find the side lengths.
First, let's substitute equation 3 into equation 2:
a + b - 2 = a + 2
Now, subtract a from both sides:
b - 2 = 2
Next, add 2 to both sides:
b = 4
Now, substitute the value of b into equation 1:
a + 4 + c = 12
Rearrange the equation:
a + c = 8
Finally, substitute the value of a + 2 into equation 3:
a + 2 = a + b - 2
Simplify:
2 = b
Therefore, the values of a, b, and c are 4, 2, and 6 respectively.
The side lengths of the triangle are 4 inches, 2 inches, and 6 inches.
To find the side lengths of the triangle, let's assign variables to the sides. Let the longest side be represented by "L", the second longest side be represented by "M", and the shortest side be represented by "S".
We are given two conditions:
1. The perimeter of the triangle is equal to 12 inches.
2. The length of the longest side (L) is equal to the sum of the other two sides (M+S) minus 2.
From the first condition, we know that the sum of all three sides is equal to 12:
L + M + S = 12
From the second condition, we know that L = M + S - 2:
L = M + S - 2
We are also given an additional condition:
If you add 2 to the shortest side (S), it will equal the longest side (L).
Using the given information, we can now solve for the side lengths.
Substituting the second condition into the first equation, we have:
(M + S - 2) + M + S = 12
2M + 2S - 2 = 12
2M + 2S = 14
M + S = 7
From here, we can use substitution to solve for the side lengths.
If we add 2 to the shortest side (S), it will equal the longest side (L):
S + 2 = L
Substituting M + S = 7 into the above equation:
M + (7 - M) = L
7 = L
Therefore, the length of the longest side (L) is 7 inches.
Now we can solve for the remaining side lengths.
Substituting L = 7 into M + S = 7:
M + S = 7
M + S = 7
M + S = 7
Since we have two unknown variables and one equation, we cannot determine unique side lengths. However, we can consider possible solutions:
- If M = 3 and S = 4: This satisfies M + S = 7.
- If M = 1 and S = 6: This also satisfies M + S = 7.
Therefore, two possible sets of side lengths could be:
M = 3, S = 4, and L = 7
or
M = 1, S = 6, and L = 7
Please note that these are just two possible solutions, and there might be other valid sets of side lengths that satisfy the given conditions.