A) 380 \[{{m}^{2}}\]
B) 370\[{{m}^{2}}\]
C) 374 \[{{m}^{2}}\]
D) 384\[{{m}^{2}}\]
Correct Answer: D
Solution :
(d): Let ABCD be the rhombus of perimeter 80 m and diagonal \[AC=24\]m We have, \[AB+BC+CD+DA=80\] \[\Rightarrow \]\[4AB=80\] \[\left[ \therefore A.B=BC=CD=DA\text{ } \right]\] \[\Rightarrow \]\[AB=20\]m In \[\Delta ABC\], we have \[2s=AB+BC+AC=20+20++24=64\] \[\Rightarrow s=32\] \[\therefore \]\[{{\Delta }_{1}}=Area\,of\,\Delta ABC=\sqrt{32\times 12\times 12\times 8}\]\[=16\times 12=192\,{{m}^{2}}\] Hence, area of rhombus \[ABCD=2\times 192\,{{m}^{2}}=384\,{{m}^{2}}\].You need to login to perform this action.
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