Draw a rectangle on a coordinate plane that has a perimeter of 16 units. Label all the vertica with they coordinate. Then find the area if he rectangle
plural of vertex is vertices.
So, draw a rectangle where the length + width = 8.
To draw a rectangle on a coordinate plane with a perimeter of 16 units, we need to determine the dimensions of the rectangle.
Let's assume the length of the rectangle is represented by "l" units, and the width is represented by "w" units.
According to the given information, the perimeter of the rectangle is 16 units. The formula for the perimeter of a rectangle is P = 2(l + w).
Substituting the given value, we have:
16 = 2(l + w)
We can simplify this equation:
8 = l + w
Since we know that the perimeter is the sum of all sides, we can assume that two sides are equal in length. Therefore, we can consider l = w.
Plugging in this assumption, we have:
8 = 2l
Dividing by 2, we find:
l = 4
So, the length of the rectangle is 4 units, and the width is also 4 units.
Now, let's draw the rectangle on the coordinate plane:
(0,4) --------- (4,4)
| |
| |
| |
(0,0) --------- (4,0)
To find the area of the rectangle, we multiply the length by the width:
Area = length × width
= 4 × 4
= 16 square units.
Therefore, the area of the rectangle is 16 square units.
To draw a rectangle on a coordinate plane with a perimeter of 16 units, we need to consider that a rectangle has two pairs of equal sides. Let's assume the width of the rectangle is x units and the length is y units.
Since the perimeter is the sum of all sides, we can determine that:
Perimeter = 2x + 2y = 16
Now, we can solve this equation to find the possible values of x and y. First, isolate one variable:
2x = 16 - 2y
Next, divide both sides by 2:
x = 8 - y/2
We can now create a table to represent the possible values of x and y:
y | x = 8 - y/2
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0 | 8 - 0/2 = 8
1 | 8 - 1/2 = 7.5
2 | 8 - 2/2 = 7
3 | 8 - 3/2 = 6.5
4 | 8 - 4/2 = 6
Based on the table, we can see that the only whole number values for x and y that satisfy the perimeter condition are x = 6 and y = 4. Therefore, the rectangle's width is 6 units, and its length is 4 units.
Now, let's draw the rectangle on the coordinate plane:
| -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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4 | . . . . . .
3 | . .
2 | . .
1 | . .
0 | . . . . . .
The area of a rectangle is calculated by multiplying the length by the width. In this case, the area is:
Area = length * width = 4 * 6 = 24 square units.
So, the area of the rectangle on the coordinate plane is 24 square units.