[tex]\huge\mathfrak{\underline{Answer:}}[/tex]
[tex]\large\bf{=20 }[/tex]
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[tex]\large\bf{\underline{Given:}}[/tex]
- A trapezium ABDE with sides 38 , 16 , 50 and x
[tex]\large\bf{\underline{To\: find :}}[/tex]
[tex]\large\bf{\underline{Construction:}}[/tex]
[tex]\setlength{\unitlength}{0.8cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf 12}\put(2.8,.3){\large\bf 16}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf D}\put(.8,.3){\large\bf C}\put(5.8,.3){\large\bf E}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf $\Theta$}\end{picture}[/tex]
[tex]\setlength{\unitlength}{0.75cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 16 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 38 cm}\put(-0.5,-0.4){\bf B}\put(-0.5,3.2){\bf C}\put(5.3,-0.4){\bf A}\put(5.3,3.2){\bf E}\end{picture}[/tex]
[tex]\large\bf{\underline{Hence,}}[/tex]
⟹CD = 50 - 38
⟹CD = 50 - 38
⟹CD = 12
[tex]\large\bf{Since,}[/tex]
- AB || CE And ABDE is a trapezium , Therefore ABCE is a rectangle
[tex]\large\bf{\underline{Therefore}}[/tex]
⟹ CE = 16
[tex]\large\bf{\underline{In\: triangle\:DCE}}[/tex]
[tex]{\large\bf{Using\: Pythagoras\: theorem:}[/tex]
[tex]\boxed{\large\bf\pink{DE^2 = CD^2 + CE^2}}[/tex]
[tex]\large\bf{⟹x^2 = 12^2 + 16^2}[/tex]
[tex]\large\bf{⟹x^2 = 144 + 256}[/tex]
[tex]\large\bf{⟹x^2 = 400}[/tex]
[tex] \large \bf \:⟹ {x} = \sqrt{400} [/tex]
[tex]\boxed{\large\bf{⟹x= 20}}[/tex]
