Use the formulas for the area and perimeter of a rectangle to solve this problem.
Draw a rectangle that has:
an area of 42 square centimeters
a perimeter of 26 centimeters
The point on the grid represents one vertex of this rectangle.
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To find the dimensions of the rectangle, we will use the given area and perimeter formulas. For a rectangle, the area (A) is equal to the product of its length (L) and width (W), and the perimeter (P) is equal to twice the sum of its length and width.
A = L * W
P = 2 * (L + W)
We are given:
A = 42 sq. cm
P = 26 cm
Now we need to find the length and the width of the rectangle.
Since A = L * W, we can write:
42 = L * W
-> L = 42 / W
Substitute this into the perimeter formula:
26 = 2 * (L + W)
-> 13 = L + W
-> W = 13 - L
Substitute L from the first equation:
W = 13 - (42 / W)
-> W^2 = 13W - 42
-> W^2 - 13W + 42 = 0
Now, we need to solve this quadratic equation for W. The factors of the equation are (W-6)(W-7)=0
So, W = 6 or 7
Since L = 42 / W and L can't be equal to W (because it's a rectangle), when W is 6, then L is 7; and when W is 7, then L is 6.
Thus, there are two possible rectangles with an area of 42 sq. cm and a perimeter of 26 cm:
1. Width = 6 cm, Length = 7 cm
2. Width = 7 cm, Length = 6 cm
Now, we can draw the rectangle on a grid as follows:
- Choose any point on the grid as one vertex.
- From that vertex, draw a horizontal line with the length (6 cm) and a vertical line with the width (7 cm).
- Connect the ends of the horizontal and vertical lines to form the rectangle.