Final answer:
The length of the shorter piece of a 100-inch board cut where one piece is three times longer than the other is 25 inches.
Step-by-step explanation:
To find the length of the shorter piece when a 100-inch board is cut into two pieces where one piece is three times the length of the other, we can first let the length of the shorter piece be x inches. Therefore, the length of the longer piece would be 3x inches. Since the total length of the board is 100 inches, we can set up the following equation:
x + 3x = 100
Solving for x, we combine like terms:
4x = 100
Divide both sides by 4 to find the value of x:
x = 100 / 4
x = 25
So, the length of the shorter piece is 25 inches.