1. The perimetre of a rhombus in 20 cm and one of the diagonal is 8 cm. What is the area (in $$cm^{2}$$) of the rhombus?
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By: anil on 05 May 2019 02.28 am
Given : ABCD is the rhombus whose diagonals bisect at O and the diagonals of a rhombus bisect each other at right angle. BD = 8 cm => OB = 4 cm Perimeter of rhombus = 20 cm => BC = $$frac{20}{4}=5$$ cm Thus, in $$ riangle$$ BOC, => $$(OC)^2=(BC)^2-(OB)^2$$ => $$(OC)^2 = (5)^2-(4)^2$$ => $$(OC)^2=25-16=9$$ => $$OC=sqrt{9}=3$$ cm Thus, AC = 6 cm and BD = 8 cm $$ herefore$$ Area of rhombus = $$frac{1}{2} imes d_1 imes d_2$$ = $$frac{1}{2} imes6 imes8=24$$ $$cm^2$$ => Ans - (B)
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