The shorter side of a triangle is 5 inches less than the medium size side. The larger side is 12 inches more than the medium size side. If the perimeter of the triangle is 40 inches, find the size of each side of the triangle. Show your work
x+12+x-5+x=40
3x+7=40
3x=33
x=11
x-5+6
x+12=23
23, 11, 6
Let m = the length of the medium sized side.
m + m - 5 + m + 12 = 40
3m + 7 = 40
3m = 33
m = ?
To find the size of each side of the triangle, let's start by assigning variables to the sides. Let's say the medium side is represented by "x" inches.
According to the given information, the shorter side is 5 inches less than the medium size side, so we can represent it as "x - 5" inches.
Similarly, the larger side is 12 inches more than the medium size side, so it can be represented as "x + 12" inches.
The perimeter of a triangle is the sum of all its sides. In this case, it is given as 40 inches. Therefore, we can set up an equation to represent the perimeter:
x + (x - 5) + (x + 12) = 40
Simplifying the equation, we get:
3x + 7 = 40
Subtracting 7 from both sides, we have:
3x = 33
Now, divide both sides by 3:
x = 11
So, the medium side is 11 inches.
Substituting this value back into our initial equations, we can find the lengths of the other sides:
Shorter side: x - 5 = 11 - 5 = 6 inches
Larger side: x + 12 = 11 + 12 = 23 inches
Therefore, the lengths of the sides of the triangle are 6 inches, 11 inches, and 23 inches.