• # question_answer In the given fig. what is the ratio of the areas of (a) shaded portion I to shaded portion II? (b) shaded portion II to shaded portion III? (c) shaded portions I and II taken together and shaded portion III?

 By splitting the above figure, we get, (a) Now,    $~AD=5$ $AB=AEBE=105$ $AB=5$ Area of shaded portion I = Area of ABCD $\therefore$  Area of $ABCD=AD\times AB=5\times 5=25$ So, Area of shaded portion $I=25$ Area of shaded portion II = Area of DCIJ ? Area FHI Now,                 $DJ=AJAD=105=5$ $DC=AB$(as It?s a square) $DC=5$ of                     $DCIJ=DJ\times DC=5\times 5=25$ Now,                 $AJ=EH$    (side of a square) $EH=10$ So,                   $FH=EHEF=107$ $FH=3$ and                   $GF=BE$ $GF=5$ area                  $GFHI=GF\times FH$ $=5\times 3=15$ Area o shaded portion $II=25+15=40$ So, required ratio of shaded portion I to II is $25:40$ $=\frac{25}{40}=\frac{5\times 5}{8\times 5}$ $=\frac{5}{8}=5:8$ (b) Area of shaded portion III = Area of BEFG $=BE\times EF$ $=5\times 7$ $=35$ So, required ratio of shaded portion II to III is $40:35$ $=\frac{40}{35}=\frac{8\times 5}{7\times 5}=\frac{8}{7}$ $=8:7$ (c) Area of shaded portions I and II = 25 + 40 = 65 So, required ratio $=65:35$ $=\frac{65}{35}=\frac{13\times 5}{7\times 5}=\frac{13}{7}$ $=13:7$