A triangular pennant has two sides the same length. The third side is 9 in. shorter than either of the equal sides. The perimeter of the pennant is 57 in. How long is the shortest side?
Let x = a longer side
2x + x - 9 = 57
3x = 57 + 9
3x = 66
x = 22
Let x = a longer side
2x + x - 9 = 57
3x = 57 + 9
3x = 66
x = 22
22 - 9 = 13
The shorter side is 13 inches long.
Let's assume the length of the equal sides of the triangular pennant is represented by 'x'.
According to the given information, the third side is 9 in. shorter than either of the equal sides. This means the length of the third side is 'x - 9'.
The perimeter of the pennant is the sum of the lengths of all three sides. In this case, it is given as 57 in.
So, we can write the equation as:
x + x + (x - 9) = 57
Combine like terms:
3x - 9 = 57
Add 9 to both sides:
3x = 66
Divide both sides by 3:
x = 22
Therefore, the length of the equal sides is 22 inches.
Now, let's find the length of the shortest side (third side):
x - 9 = 22 - 9 = 13
So, the length of the shortest side is 13 inches.
To solve this, we need to set up an equation based on the information provided.
Let's denote the length of the equal sides as "x" and the length of the shortest side as "y".
We know that the third side is 9 inches shorter than either of the equal sides, so we can express it as "x - 9".
The perimeter of a triangle is the sum of all its sides. In this case, it is given as 57 inches.
So, the equation we can set up is:
x + x + (x - 9) = 57
Combining like terms, we simplify the equation to:
3x - 9 = 57
Next, we isolate the variable by adding 9 to both sides:
3x = 66
Finally, we solve for x by dividing both sides by 3:
x = 22
Now, we know that the length of the equal sides (x) is 22 inches.
To find the length of the shortest side (y), we substitute x back into the expression "x - 9":
y = 22 - 9
y = 13
Hence, the shortest side of the triangular pennant is 13 inches.