The perimeter of a triangle is 42 yards. The first side is 5 yards less than the second side, and the third side is 2 yards less than the first side. What is the length of each side?
To solve this problem, we can set up equations based on the given information. Let's call the first side of the triangle "x" yards.
According to the given information, the second side is 5 yards longer than the first side, so the length of the second side is (x + 5) yards.
The third side is 2 yards less than the first side, so the length of the third side is (x - 2) yards.
The perimeter of a triangle is the sum of all its sides. In this case, we know that the perimeter is 42 yards, so we can write the equation:
x + (x + 5) + (x - 2) = 42
Now we can solve for x:
3x + 3 = 42
3x = 39
x = 13
Therefore, the first side of the triangle is 13 yards.
To find the length of the second side:
x + 5 = 13 + 5 = 18
So, the second side is 18 yards.
To find the length of the third side:
x - 2 = 13 - 2 = 11
Therefore, the third side is 11 yards.
In conclusion, the length of each side of the triangle is 13 yards, 18 yards, and 11 yards.
sides are
x
x-5
x-7
so
3x-12 = 42
3x = 54
x = 16 etc