1. In figure, DE || BC. If DE = 3 cm, BC = 6 cm and area of ΔADE = 15 sq cm, then the area of ΔABC is
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By: anil on 05 May 2019 01.49 am
It is given thatDE = 3 cm, BC = 6 cm Let area of $$ riangle$$ ABC = $$x$$ sq cm and area of $$ riangle$$ ADE = 15 sq cm
In $$ riangle$$ ADE and $$ riangle$$ ABC $$angle$$ DAE = $$angle$$ BAC (common) $$angle$$ ADE = $$angle$$ ABC (Alternate interior angles) $$angle$$ AED = $$angle$$ ACB (Alternate interior angles) => $$ riangle$$ ADE $$sim$$ $$ riangle$$ ABC => Ratio of Area of $$ riangle$$ ADE : Area of $$ riangle$$ ABC = Ratio of square of corresponding sides = $$(DE)^2$$ : $$(BC)^2$$ => $$frac{15}{x}=frac{(3)^2}{(6)^2}$$ => $$frac{15}{x} = frac{9}{36}$$ => $$frac{15}{x}=frac{1}{4}$$ => $$x=15 imes4=60$$ $$cm^2$$ => Ans - (D)
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In $$ riangle$$ ADE and $$ riangle$$ ABC $$angle$$ DAE = $$angle$$ BAC (common) $$angle$$ ADE = $$angle$$ ABC (Alternate interior angles) $$angle$$ AED = $$angle$$ ACB (Alternate interior angles) => $$ riangle$$ ADE $$sim$$ $$ riangle$$ ABC => Ratio of Area of $$ riangle$$ ADE : Area of $$ riangle$$ ABC = Ratio of square of corresponding sides = $$(DE)^2$$ : $$(BC)^2$$ => $$frac{15}{x}=frac{(3)^2}{(6)^2}$$ => $$frac{15}{x} = frac{9}{36}$$ => $$frac{15}{x}=frac{1}{4}$$ => $$x=15 imes4=60$$ $$cm^2$$ => Ans - (D)