Dahlia wants to build a sandbox that has a perimeter of 26 meters. The length is 7 meters.
What is the width of their sandbox?
The correct answer and explanation is:
To find the width of the sandbox, we will use the formula for the perimeter of a rectangle: P=2L+2WP = 2L + 2W
Where:
- PP is the perimeter,
- LL is the length, and
- WW is the width.
We are given:
- The perimeter P=26P = 26 meters,
- The length L=7L = 7 meters.
Now, plug the values into the formula: 26=2(7)+2W26 = 2(7) + 2W
Simplifying: 26=14+2W26 = 14 + 2W
To isolate WW, subtract 14 from both sides: 26−14=2W26 – 14 = 2W 12=2W12 = 2W
Next, divide both sides by 2 to solve for WW: W=122=6W = \frac{12}{2} = 6
So, the width of the sandbox is 6 meters.
Explanation:
The formula for the perimeter of a rectangle gives the total distance around the four sides. Since the perimeter is the sum of all the sides, it is helpful to break down the calculation into manageable parts. By substituting the known values for the perimeter and length, we can isolate the unknown width. By carefully solving the equation step by step, we determine that the width of the sandbox is 6 meters. This process shows how basic algebraic manipulation can solve geometry problems involving perimeter.