We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
424
3
avatar+1438 

https://web2.0calc.com/questions/in-depth-answers-would-be-greatly-appreciated

 

Thanks so much!

 Mar 20, 2018
 #1
avatar+22263 
+2

The diagonals of a trapezoid are perpendicular and have lengths 8 and 10.

Find the length of the median of the trapezoid.

 

Area A = ?

\(\begin{array}{|rcll|} \hline 2A &=& (8-y)x + xy + (10-x)y+(10-x)(8-y) \\ 2A &=& 8x-yx+xy+10y-xy+80-10y-8x+xy \\ 2A &=& 80 \\ \mathbf{A} & \mathbf{=} & \mathbf{40} \\ \hline \end{array}\)

 

h = ?

\(\begin{array}{|rclrcl|} \hline \sin(B) &=& \dfrac{h}{8} & \sin(A) &=& \dfrac{h}{10} \quad & | \quad B = 90^{\circ}-A \\ \sin(90^{\circ}-A)^2+ \sin(A)^2 &=& \dfrac{h^2}{8^2} +\dfrac{h^2}{10^2} \\ \cos(A)^2+ \sin(A)^2 &=& \dfrac{h^2}{8^2} +\dfrac{h^2}{10^2} \\ 1 &=& \dfrac{h^2}{8^2} +\dfrac{h^2}{10^2} \\ \dfrac{h^2}{8^2} +\dfrac{h^2}{10^2} &=& 1 \\ h^2\left( \dfrac{1}{8^2} + \dfrac{1}{10^2} \right) &=& 1 \\ h^2\left( \dfrac{164}{8^210^2} \right) &=& 1 \\ h &=& \dfrac{8\cdot 10}{\sqrt{164}} \\ h &=& \dfrac{8\cdot 10}{\sqrt{4\cdot 41}} \\ h &=& \dfrac{8\cdot 10}{2\sqrt{41}} \\ \mathbf{ h }&\mathbf{=}& \mathbf{\dfrac{40}{\sqrt{41}} } \\ \hline \end{array}\)

 

median m = ?

\(\begin{array}{|rcll|} \hline A &=& \dfrac{a+c}{2} \cdot h \quad & | \quad m = \dfrac{a+c}{2}\\\\ A &=& m \cdot h \\\\ m &=& \dfrac{A}{h} \\\\ m &=& \dfrac{40}{ \dfrac{40}{\sqrt{41} } } \\\\ m &=& \dfrac{40}{40}\cdot \sqrt{41} \\\\ m &=& \sqrt{41} \\\\ \mathbf{ m} &\mathbf{ =} & \mathbf{ 6.40312423743} \\ \hline \end{array} \)

 

 

laugh

 Mar 20, 2018
edited by heureka  Mar 20, 2018
 #2
avatar+1438 
+4

Thanks so much for your answer Heaureka, that's some impressive Latex!

AnonymousConfusedGuy  Mar 20, 2018
 #3
avatar+101729 
+2

Sorry guys, I had failed to seet he word 'perpendicular' in the question.

I better get some new specs.

 

Thanks Heureka :)

Melody  Mar 21, 2018
edited by Melody  Mar 21, 2018

19 Online Users

avatar
avatar
avatar