Question

Given SU = 10. VX = 44 and TW = 2x – 1, find the value of x and the length of the median TW in Trapezoid SUXV.

Answer 1

The Solution.

By Similarity Theorem, we have that Trapezoid SUTW is congruent to trapezoid TWVX.

So,

$\begin{gathered} \frac{SU}{TW}=\frac{TW}{VX} \\ \text{Where SU=10} \\ VX=44\text{ , TW=2x-1} \end{gathered}$

Substituting these values into the ratio above, we get

$\frac{10}{2x-1}=\frac{2x-1}{44}$

Cross multiplying, we get

$\begin{gathered} (2x-1)^2=44\times10 \\ (2x-1)^2=440 \\ \text{Square rooting both sides, we get} \\ 2x-1=\sqrt[]{440} \\ 2x-1=\pm20.976 \end{gathered}$$\begin{gathered} 2x=1\pm20.976 \\ \text{Dividing both sides by 2, we get} \\ x=\frac{1\pm20.976}{2} \\ \\ x=\frac{1+20.976}{2}=\frac{21.976}{2}=10.988 \\ Or \\ x=\frac{1-20.976}{2}=-9.988\text{ but x cannot be negative.} \end{gathered}$

So, the correct value of x is 10.988

To find the length TW:

We substitute 10.988 for x in 2x-1

$\begin{gathered} TW=2(10.988)-1 \\ \text{ =21.976-1} \\ \text{ =20.976}\approx21 \end{gathered}$

Thus, the correct answer is:

x = 10.988

TW = 20.976