Two sides of a triangles are equal in length. the length of the third side is three meters less than the sum of the lengths of the other two sides. What is the length of the longest side of the trangle if its perimeter is 29 meter?
S=2L-3
29=S+2L=2l-3+2l= 4L-3
4L=32
L=8
sides: 8,8, 13
Let's call the length of the equal sides x.
According to the given information, the length of the third side is (x + x) - 3 = 2x - 3.
The perimeter of a triangle is the sum of all three sides, so we have x + x + (2x - 3) = 29.
Combining like terms, we get 4x - 3 = 29.
Adding 3 to both sides, we have 4x = 32.
Dividing both sides by 4, we find x = 8.
Therefore, the length of the longest side is 2x - 3 = 2(8) - 3 = 16 - 3 = 13 meters.
To solve this problem, we can use the information given and apply the properties of triangles.
Let's first assign variables to the lengths of the equal sides of the triangle. We can call this length "x". Since two sides of the triangle are equal, we have two sides of length "x".
The length of the third side is given to be three meters less than the sum of the lengths of the other two sides. So, the length of the third side is (2x - 3).
We know that the perimeter of a triangle is the sum of all its side lengths. In this case, the perimeter is given to be 29 meters.
To find the length of the longest side, we need to determine the value of "x". So, we can set up the equation:
2x + (2x - 3) = 29
Simplifying the equation, we have:
4x - 3 = 29
Add 3 to both sides:
4x = 32
Divide both sides by 4:
x = 8
Therefore, the length of each equal side is 8 meters.
To find the longest side, we substitute the value of "x" into the expression for the length of the third side:
2x - 3 = 2(8) - 3 = 13
So, the length of the longest side of the triangle is 13 meters.