The quadrilateral WXYZ is a parallelogram WT=10cm and XT=2cm what is XZ
Since WXYZ is a parallelogram, we know that opposite sides are equal in length.
Therefore, we have:
XZ = WT = 10cm (since WT is opposite to XZ)
And,
XZ = XT + TZ (where TZ is the length of ZT)
We know that XT = 2cm from the given information.
To find TZ, we can use the fact that WXYZ is a parallelogram, so the opposite sides are parallel.
Therefore:
XT is parallel to WZ
And,
WT is parallel to XY
This means that angles WXT and ZXT are congruent, and angles XWT and XZY are congruent.
Since the sum of angles in a triangle is 180 degrees, angles WXT and XZY add up to 180 degrees.
Therefore:
WXT + XZY = 180
And since WXT and ZXT are congruent, we have:
2WXT = 180
WXT = 90 degrees
This means that triangle XWT is a right triangle with angle XWT equal to 90 degrees.
Using the Pythagorean theorem, we can find the length of ZT:
(XT)^2 + (ZT)^2 = (WT)^2
Substituting the given values, we get:
2^2 + (ZT)^2 = 10^2
4 + (ZT)^2 = 100
(ZT)^2 = 96
ZT = √96 = 4√6
Therefore:
XZ = XT + TZ = 2 + 4√6 cm.