On the coordinate plane, the segment from D(-1,-17) to E(14,19) forms one side of a rectangle. The rectangle has an area of 546 square units. Find the perimeter of the rectangle.
Write your answer as a whole number, decimal, or simplified radical. Do not round
the length of DE is √((14+1)^2 + (19+17)^2) = 39
the adjacent side is 546/39 = 14
so the perimeter is 2(39+14) = ____
Well, let's calculate the length of the segment DE first. We can use the distance formula for that: √((x₂ - x₁)² + (y₂ - y₁)²).
Plugging in the coordinates, we get √((14 - (-1))² + (19 - (-17))² = √(15² + 36²) = √(225 + 1296) = √1521 = 39.
Now, since DE is one side of the rectangle, the other side is also 39.
To find the dimensions of the rectangle, we can use the formula Area = Length × Width. We know that the area is 546, so 546 = 39 × Width. Solving for Width, we get Width = 546/39 = 14.
Therefore, the dimensions of the rectangle are 39 units by 14 units.
Now, to find the perimeter, we need to add up all the sides of the rectangle. Since opposite sides are equal in a rectangle, we just need to multiply the length and width by 2 and add them up.
Perimeter = 2(39 + 14) = 2(53) = 106.
So, the perimeter of the rectangle is 106 units.
To find the perimeter of the rectangle, we need to know the lengths of its sides.
The length of the side DE can be found using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, (x1, y1) = (-1, -17) and (x2, y2) = (14, 19).
Using the distance formula:
DE = √((14 - (-1))^2 + (19 - (-17))^2)
= √((15)^2 + (36)^2)
= √(225 + 1296)
= √1521
= 39 units
Now, let's find the width of the rectangle.
The area of a rectangle is given by the formula:
Area = Length * Width
In this case, we know that the area is 546 square units, and the length is 39 units.
So, we can solve for the width:
546 = 39 * Width
Width = 546/39
Width = 14 units
Since a rectangle has opposite sides of equal length, the other side of the rectangle will also have a length of 39 units.
Now, we can find the perimeter of the rectangle by summing up the lengths of all its sides:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (39 + 14)
Perimeter = 2 * 53
Perimeter = 106 units
Therefore, the perimeter of the rectangle is 106 units.
To find the perimeter of the rectangle, we need to determine the length and width of the rectangle first.
To find the length of the rectangle, we can use the distance formula. The distance formula is √((x2-x1)^2 + (y2-y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the length is the distance between points D(-1, -17) and E(14, 19).
Length = √((14 - (-1))^2 + (19 - (-17))^2)
= √((15)^2 + (36)^2)
= √(225 + 1296)
= √1521
= 39
To find the width of the rectangle, we equate the area of the rectangle to the product of its length and width. We can then solve for the width.
Area = length * width
546 = 39 * width
width = 546 / 39
width = 14
Now that we have the length and width of the rectangle, we can calculate the perimeter.
Perimeter = 2 * (length + width)
Perimeter = 2 * (39 + 14)
Perimeter = 2 * 53
Perimeter = 106
Therefore, the perimeter of the rectangle is 106 units.