Math, asked by ΙΙïƚȥΑαɾყαɳΙΙ, 5 hours ago

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Answered by OoAryanKingoO78

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Area covered by wiper=area of arc(A0D)+area of traingleAOB+area of arc(BOC)

We know AO and OB are wipers,whose lengths are 1.5

In ∆ABC

AB^2+BC^2=AC^2

(1.5√3)^2+(1.5)^2=(AC)^2

2.25×3+2.25=(AC)^2

2.25×4=AC^2

AC=3

Also AO=1.5

similarly using Pythagoras theorem in ∆OBC

we get

OC=1.5

this shows that point O is the bisector of diagonal AC

so,AO=OC

also from property of rectangle we know that, diagonal bisects each other equally

so,O will also be the bisector of diagonal BD

hence OB=OD=1.5

AC=BD (property of triangle)

AC/2=BD/2

OB=OC,hence OB=OC=OD=OA=1.5=AD=BC

Hence OAD will be an equilateral triangle

angle OAD=60

similarly angleOBC=60

area of sector=angle of that sector ×area of circle/360

area of arc(AOD)+arc(BOC)=60/360 ×3.14 ×1.5×1.5 +60/360 ×3.14×1.5×1.5

=2×(60/360)×1.5×1.5

area of triangleAOB=area of rectangle/4 (diagonal divides the rectangle in 4 equal parts)

area of triangle=1.5×1.5√3/4

=>1.5×2.6/4=3.90/4

=0.975 or 0.98(approx)

Area covered by wiper=.98+2×60/360 ×3.14×1.5×1.5

=.98+0.75×3.14=2.35+0.97

=2.35+.98

Percentage of area of windshield covered by wiper=3.3×100/3.9=84.61

hence percentage of area of windshield covered by wiper is 85percent(approx)