A) 8m
B) 10m
C) 15m
D) 4m
Correct Answer: B
Solution :
Let the length of non-parallel sides AD and BC be x m. Here AB||CD and AB=20m, CD=36m Area of trapezium \[ABCD=168{{m}^{2}}\] Let the distance between two parallel sides be \[h\]. \[\therefore \]\[168=\frac{1}{2}\times (AB+CD)\times h\] \[168=\frac{1}{2}\times 56\times h\Rightarrow h=6m\] Now draw \[\text{BE }\!\!|\!\!\text{ }\!\!|\!\!\text{ AD}\] Given, \[\text{AB }\!\!|\!\!\text{ }\!\!|\!\!\text{ CD}\Rightarrow \text{AB }\!\!|\!\!\text{ }\!\!|\!\!\text{ DE}\] \[\therefore \] ABED is a parallelogram. \[\Rightarrow BE=AD=x\] and \[AB=DE=20m\] So, \[EC=36-20=16m\] In \[\Delta BEC,\] we have \[BE=BC=x\,\,m\] \[\Rightarrow \Delta BEC\] is an isosceles triangle. \[\therefore \]\[EM=MC=\frac{1}{2}EC=\frac{1}{2}\times 16=8m\] By Pythagoras theorem in \[\Delta BEM,\] \[B{{E}^{2}}=B{{M}^{2}}+E{{M}^{2}}\] \[\Rightarrow {{x}^{2}}={{6}^{2}}+{{8}^{2}}=100\Rightarrow x=10m\] Hence, the length of non-parallel side is 10m.You need to login to perform this action.
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