A fence surrounds a square plot of land. The area is 324 yd 2. Find the length of each side.
Use the Systematic Guess and Check method.
What I already know:
It is a square shape. And all squares have equal sides.
Right.
So what is the length of each side?
Is it 81?
81 * 81 = 6,561
Obviously that's not right.
What is the square root of 324?
18
Right.
Is it 81?
To find the length of each side of the square plot of land, we can use the Systematic Guess and Check method.
Step 1: Start with a reasonable guess for the length of one side. Let's say, 10 yards.
Step 2: Calculate the area of the square. Since the area is given as 324 yd^2, we can multiply the length of one side by itself: 10 * 10 = 100 yd^2.
Step 3: Compare the calculated area with the given area. In this case, the calculated area (100 yd^2) is less than the given area (324 yd^2).
Step 4: Adjust the guess accordingly. Since the calculated area is less than the target area, we need a larger side length. Let's try 15 yards.
Step 5: Calculate the area again using the new guess. 15 * 15 = 225 yd^2.
Step 6: Compare the calculated area to the given area. The new calculated area (225 yd^2) is still less than the given area (324 yd^2).
Step 7: Repeat steps 4-6 until the calculated area matches the given area.
Let's continue the systematic guess and check process:
Guess: 20 yards
Calculated area: 20 * 20 = 400 yd^2 (greater than the given area)
Guess: 17 yards
Calculated area: 17 * 17 = 289 yd^2 (less than the given area)
Guess: 18 yards
Calculated area: 18 * 18 = 324 yd^2 (matches the given area)
So, the length of each side of the square plot of land is 18 yards.