One side of a triangle is 3 inches shorter than twice the length of the shortest side. The third side is 5 inches longer than the shortest side. If the perimeter is 110 inches, find the lengths of all three sides. So what are all the three sides?
if the shortest side is s,
s + (2s-3) + (s+5) = 110
To solve this problem, let's assign variables to represent the lengths of the three sides of the triangle.
Let:
x = length of the shortest side
2x - 3 = length of one side
x + 5 = length of the remaining side
Given that the perimeter of the triangle is 110 inches, we can set up an equation:
x + (2x - 3) + (x + 5) = 110
Combining like terms, we have:
4x + 2 = 110
Subtracting 2 from both sides, we get:
4x = 108
Divide both sides by 4 to solve for x:
x = 27
Now we can find the lengths of all three sides:
Shortest side = x = 27 inches
One side = 2x - 3 = 2(27) - 3 = 51 inches
Remaining side = x + 5 = 27 + 5 = 32 inches
So, the lengths of the three sides are 27 inches, 51 inches, and 32 inches.