Math, asked by hleema, 3 months ago

Roshan wants to buy a trapizium shaped field .its side along the river is parallel to and twice the side along the road . If the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m . find the length of the side along the river​

Answers

Answered by BrainlyRish
64

Given : Area of The Trapezium shaped Field is 10,500 m² , Height or Distance between parallel sides of Trapezium shaped field is 100 m & Other Parallel side or the side along the river is twice the side along the road .

Exigency to find : The Length of the other parallel side or side along the river of Trapezium shaped field.

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❍ Let's Consider the side of along the road or one parallel side be x m .

Given that ,

  • Other Parallel side or the side along the river is twice the side along the road .

Therefore,

  • The Other Parallel side or side along the river is 2x m.

\dag\:\:\it{ As,\:We\:know\:that\::}\\

\qquad \dag\:\:\bigg\lgroup \sf{Area _{(Trapezium)} \:: \dfrac{1}{2} \times (a + b) \times h  }\bigg\rgroup \\\\

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⠀⠀⠀⠀Here a & b are two parallel sides of Trapezium, h is the Height or Perpendicular distance between parallel side of Trapezium & we have been given with the Area of Trapezium is 10,500 m² .

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⠀⠀⠀⠀⠀⠀\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\

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\qquad \longmapsto \sf 10,500 = \dfrac{1}{2} \times (2x + x ) \times 100 \\\\

\qquad \longmapsto \sf 10,500 = \dfrac{1}{\cancel {2}} \times (2x + x) \times \cancel {100} \\\\

\qquad \longmapsto \sf 10,500 =  (2x + x ) \times 50 \\\\

\qquad \longmapsto \sf 10,500 =  (3x) \times 150 \\\\

\qquad \longmapsto \sf 10,500 = 150x \\\\

\qquad \longmapsto \sf \cancel {\dfrac{10,500}{150}} = x \\\\

\qquad \longmapsto \sf 70 = x \\\\

\qquad \longmapsto \frak{\underline{\purple{\:x = 70 \;m }} }\bigstar \\

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Therefore,

  • The Parallel Side or the Side along the road is x = 70 m
  • The other Parallel side or side along the river is 2x = 2(70) = 140 m

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Therefore,

⠀⠀⠀⠀⠀\therefore {\underline{ \mathrm {\:The\:Side\:along \:the\:River \:is\:\bf{140\:m}}}}\\

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