Question

type the correct answer in the box.
find the length of \\(overline{su}\\) in the isosceles trapezoid.
\\(sw = 1.7\\)
\\(vw = 3\\)
\\(sv = 1.5\\)
\\(tu = 1.5\\)
\\(su = \\)

Explanation:

Step1: Recall trapezoid diagonal property

In an isosceles trapezoid, the diagonals are equal, and the segments of one diagonal are proportional to the segments of the other diagonal. Here, $\frac{SW}{WU} = \frac{VW}{WT}$. Also, we can use the property that $\frac{SW}{SU} = \frac{SV}{SV + TU}$.

Step2: Substitute known values

We know $SW=1.7$, $SV=1.5$, $TU=1.5$. Let $SU = x$, so $WU = x - 1.7$.
$\frac{1.7}{x - 1.7} = \frac{1.5}{1.5}$

Step3: Solve for $x$

Since $\frac{1.5}{1.5}=1$, we get $1.7 = x - 1.7$
$x = 1.7 + 1.7$
$x = 3.4$

Answer:

3.4