Quadrilateral ABCD is similar to quadrilateral WXYZ. Side BC is 8.6 units in length, side AD is 23.1 units, and side WZ measures 15.8 units. What is the measure of side XY?
XY/BC = WZ/AD
XY/8.6 = 15.8/23.1
XY = 5.88
To find the measure of side XY in quadrilateral WXYZ, we need to use the concept of similarity of triangles.
Since quadrilateral ABCD is similar to quadrilateral WXYZ, their corresponding sides are proportional.
Let's set up a proportion using the given measurements:
BC/XY = AD/WZ
Plugging in the values we know:
8.6/XY = 23.1/15.8
Now, we can solve for XY by cross-multiplying and then dividing both sides of the equation:
8.6 * 15.8 = XY * 23.1
135.88 = XY * 23.1
Dividing both sides by 23.1:
XY = 135.88 / 23.1
XY ≈ 5.88 units
Therefore, the measure of side XY is approximately 5.88 units.
In order to find the measure of side XY, we need to use the concept of similarity between quadrilaterals.
When two quadrilaterals are similar, their corresponding sides are in proportion. This means that the ratio of the lengths of the corresponding sides of the two quadrilaterals will be the same.
In this case, we know that side BC is 8.6 units in length in quadrilateral ABCD, and side WZ is 15.8 units in length in quadrilateral WXYZ.
To find the measure of side XY, we can set up a proportion using the lengths of these two sides:
BC/AD = WZ/XY
Plugging in the given values, we have:
8.6/23.1 = 15.8/XY
To solve for XY, we can cross-multiply and then divide:
(8.6 * XY) = (23.1 * 15.8)
Dividing both sides by 8.6, we get:
XY = (23.1 * 15.8) / 8.6
Therefore, the measure of side XY is approximately 42.62 units.