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Question Number 194624 by BaliramKumar last updated on 11/Jul/23

Commented by BaliramKumar last updated on 11/Jul/23

$$\mathrm{Please}\mathrm{Help}\mathrm{only}\mathrm{answer}\mathrm{no}\mathrm{solution}$$$$\mathrm{BF}=?$$$$\mathrm{FH}=?$$$$\mathrm{HJ}=?$$$$\mathrm{JC}=?$$$$\mathrm{\&}$$$$\mathrm{AE}=?$$$$\mathrm{EG}=?$$$$\mathrm{GI}=?$$$$\mathrm{ID}=?$$

Commented by BaliramKumar last updated on 11/Jul/23

$$\mathrm{yes}\mathrm{sir}$$$$\mathrm{approx}\mathrm{answer}\mathrm{need}$$

Answered by Frix last updated on 11/Jul/23

$$\mathrm{The}\mathrm{area}\mathrm{of}ABCD\mathrm{is}\mathbb{A}=\frac{\overline{AB}+\overline{CD}}{2}\times \overline{AD}$$$$A_1=A_2=A_3=A_4=\frac{\mathbb{A}}{4}$$$$\mathrm{Put}AD\mathrm{on}\mathrm{the}x-\mathrm{axis}\mathrm{with}A=\left(0/0\right)$$$$BC:f\left(x\right)=\frac{154x}{575}+122$$$$\frac{\mathbb{A}}{4}=\underset{0}{\stackrel{a}{\int }}f\left(x\right)dx=\underset{a}{\stackrel{b}{\int }}f\left(x\right)dx=\underset{b}{\stackrel{c}{\int }}f\left(x\right)dx=\underset{c}{\stackrel{575}{\int }}f\left(xx\right)dx$$$$...\mathrm{should}\mathrm{be}\mathrm{easy}\mathrm{to}\mathrm{solve}$$

Commented by BaliramKumar last updated on 12/Jul/23

$$\mathrm{Thanks}$$

Commented by mahdipoor last updated on 12/Jul/23

$$yoursolutioniswithapproximationA=90$$$$versusmysolutionisexact$$$$itsreasonforourdifferenceanswer$$$$likeyou,igotA=90andmyanswas$$$$AE=193,41...andetc.$$

Commented by Frix last updated on 12/Jul/23

$$\mathrm{I}\mathrm{get}$$$$AE\approx 193EG\approx 148GI\approx 124ID\approx 109$$$$EF\approx 174GH\approx 213IJ\approx 247$$$$BF\approx 200FH\approx 153HJ\approx 129JC\approx 113$$

Commented by Frix last updated on 12/Jul/23

$$\mathrm{Obviously}\mathrm{we}\mathrm{have}2\mathrm{angles}\mathrm{of}90°\mathrm{at}A\mathrm{\&}D$$$$\mathrm{and}\mathrm{the}\mathrm{length}575\mathrm{is}\mathrm{an}\mathrm{approximate}\mathrm{value}.$$

Commented by mahdipoor last updated on 12/Jul/23

$$wemusttakeoneoftheA=90oralength$$$$isapproximate,$$$$mrBKandiconsiderlengthisexact,for$$$$exactansweritsimportant(whichoneisapproximatio?),$$$$butforapproximationanswernotimportant$$$$$$

Answered by mahdipoor last updated on 12/Jul/23

$$wrong:$$$$determineverticalline\left(BH\right),H\in DC$$$$BHCis\mathrm{\Delta }and\mathrm{\angle }H=90$$$${({BH}^2+{HC}^2)}^{1/2}=BC\Rightarrow$$$$BH=AD=575,HC=DC-AB=154,$$$$\Rightarrow ({575}^2+{154}^2)=595\Rightarrow 595.24...=595$$

Commented by BaliramKumar last updated on 12/Jul/23

$$\mathrm{\angle }\mathrm{A}=\mathrm{\angle }\mathrm{D}\approx 90°$$

Commented by mahdipoor last updated on 12/Jul/23

$$\mathrm{\angle }A=90+\alpha ,tan\alpha =a;\mathrm{\angle }B=90+\beta ,tan\beta =b$$$$AB=x,h_1={AH}_1,H_1\in EF;h_2={AH}_2,H_2\in GH;h_3,...$$$$A\equiv totalArea$$$$A_n=\frac{n}{4}A=\frac{x+(x+h_n(a+b))}{2}\times h_n$$$$(note:A_{n}ineq\equiv A_1+A_2+...+A_{n}inshape)$$$$\Rightarrow (a+b)h_n^2+\left(2x\right)h_n-\frac{nA}{2}\Rightarrow h_n>0$$$$h_n=\frac{-2x+\sqrt{4x^2+2nA(a+b)}}{2(a+b)}$$$$nowyoucandetermineother...$$$$inthiscase:,$$$$h_n\backsimeq 449\sqrt{.957+n}-429.82$$$$AE=h_{1}cos\alpha \backsimeq 198.3$$$$EG=AF-AE=h_{2}cos\alpha -198.3=144$$$$...$$

Commented by BaliramKumar last updated on 12/Jul/23

$$\mathrm{I}\mathrm{calculate}\mathrm{AE}=193.41\mathrm{Link}$$$$\mathrm{by}\mathrm{integration}$$

Commented by Frix last updated on 12/Jul/23

$$\mathrm{\angle }A,D\approx 90°?\mathrm{makes}\mathrm{no}\mathrm{sense}.\mathrm{In}\mathrm{this}\mathrm{case}$$$$\mathrm{the}\mathrm{horizontal}\mathrm{lines}\mathrm{cannot}\mathrm{be}\mathrm{parallel}.$$

Commented by BaliramKumar last updated on 12/Jul/23

Commented by BaliramKumar last updated on 12/Jul/23

$$$$To be divided equally among four people.

Commented by Frix last updated on 12/Jul/23

$$\mathrm{If}\mathrm{the}2\mathrm{angles}\mathrm{are}\mathrm{not}90°\mathrm{there}\mathrm{are}\mathrm{infinite}$$$$\mathrm{possibilities}\mathrm{to}\mathrm{divide}$$

Commented by BaliramKumar last updated on 12/Jul/23

$$\mathrm{yes}$$$$\mathrm{but}3\mathrm{red}\mathrm{line}\mathrm{\&}2\mathrm{side}\mathrm{line}\mathrm{should}\mathrm{be}\mathrm{approx}\mathrm{parallel}$$

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