The height of a parallelogram with an area of 300 square yards and a base of 15 yards and 1 more question A rectangle has verticles W(2,3) X (2,6) Y(7,6) and Z(7,3) Describe how to find the side lengths of the rectangle without graphing
For the parallelogram, the area is base times height
so, h * 15 = 300
the height is 20
For number 2 use the distance formula.
2,3 to 2,6 is 3 units.
2,6 to 7,6 is 5 units
7,6 to 7,3 is 3
2,3 to 7,3 is 5
So it is a rectangle 5 x 3
To find the height of a parallelogram, you need to divide the area of the parallelogram by the length of its base. In this case, the area is given as 300 square yards and the base measures 15 yards.
The formula to find the height (h) of a parallelogram is:
h = Area / Base
Substituting the given values:
h = 300 square yards / 15 yards = 20 yards
Therefore, the height of the parallelogram is 20 yards.
Now, let's move on to your second question about finding the side lengths of a rectangle with vertices W(2,3), X(2,6), Y(7,6), and Z(7,3). We can find the lengths without graphing by using the distance formula.
The distance formula can be used to find the distance (d) between two points (x1, y1) and (x2, y2) on a coordinate plane:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Applying the formula to find the side lengths:
1. Length WX:
d(W, X) = √((2 - 2)^2 + (6 - 3)^2) = √(0 + 9) = √9 = 3 units
2. Length XY:
d(X, Y) = √((7 - 2)^2 + (6 - 6)^2) = √(25 + 0) = √25 = 5 units
3. Length YZ:
d(Y, Z) = √((7 - 7)^2 + (3 - 6)^2) = √(0 + 9) = √9 = 3 units
4. Length ZW:
d(Z, W) = √((2 - 7)^2 + (3 - 3)^2) = √(25 + 0) = √25 = 5 units
Hence, the side lengths of the given rectangle are: WX = 3 units, XY = 5 units, YZ = 3 units, and ZW = 5 units.