Quadrilateral XYZW IS A RECTENGULAR. If XY+YZ=7 AND XZ+YW=10, SO FIND XY? Give answers
To find the length of XY in the given quadrilateral XYZW, we can use the given information:
1. Start by labeling the quadrilateral XYZW as shown below:
X-------Y
| |
| |
W-------Z
2. Since XYZW is a rectangular quadrilateral, we know that opposite sides are equal in length.
3. Given that XY + YZ = 7, we can substitute the length of YZ with XY in the equation, as XY = YZ.
Therefore: XY + XY = 7
2XY = 7
XY = 7/2 = 3.5
So, the length of XY is 3.5 units.
To find the length of XY in the rectangular quadrilateral XYZW, we can use the given information about the lengths of the sides.
Let's express the given information algebraically:
1. XY + YZ = 7
2. XZ + YW = 10
Since quadrilateral XYZW is rectangular, opposite sides are equal in length. So, XY is equal to ZW and YZ is equal to XW.
Let us solve for XY using these equations:
1. XY + YZ = 7
XY + XW = 7 (Substituting YZ with XW, since they are opposite sides)
XY + XZ = 7 (Rearranging the equation)
2. XZ + YW = 10
XZ + XY = 10 (Substituting YW with XY, since they are opposite sides)
Now, we have a system of equations to solve simultaneously:
XY + XZ = 7
XZ + XY = 10
If we add the two equations together, we get:
2XY + 2XZ = 17
Dividing both sides by 2, we get:
XY + XZ = 8.5
Subtracting the second equation from the first, we get:
2XZ - XY = -2.5
Now, we have two equations:
XY + XZ = 8.5
2XZ - XY = -2.5
To solve these equations, we can use the method of substitution or elimination. Let's use the elimination method to eliminate XY.
Multiply the first equation by 2:
2XY + 2XZ = 17
Now, subtract the second equation from it:
2XY + 2XZ - (2XZ - XY) = 17 - (-2.5)
Simplifying:
2XY + 2XZ - 2XZ + XY = 17 + 2.5
3XY = 19.5
Dividing both sides by 3:
XY = 6.5
Therefore, the length of XY in the rectangular quadrilateral XYZW is 6.5 units.