question_answer

Two sides of a plot measure 32 m and 24 m and angle between them is perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. The area of plot \[(in\,\,{{m}^{2}})\]\[7056\,{{m}^{2}}\] is

A)  534                 

B)  754

C)  705     

D)  684

Correct Answer: D

Solution :

[d]        Let ABCD is the plot with sides shown.  Join AC As \[\angle ABD=90{}^\circ \] \[\therefore \] \[AC=\sqrt{A{{B}^{2}}+B{{C}^{2}}}=\sqrt{{{32}^{2}}+{{24}^{2}}}\] AC = 40 m Area of \[\Delta ABC\text{=}\frac{1}{2}\times 32\times 24\,\] \[Area\,o\text{f}\,\Delta \text{ABC=384}\,{{\text{m}}^{\text{2}}}\]                    ? (1) \[Area\,o\text{f}\,\Delta \text{ACD=}\sqrt{s(s-AC)(s-CD)(s-AD)}\] S = semi perimeter of \[\Delta \text{ACD}\] \[s=\frac{25+25+40}{2}=45\] \[\therefore \,\,\,Area\,\,o\text{f}\,\Delta \text{ACD}\] \[=\sqrt{45(45-40)(45-25)(45-25)}=300{{m}^{2}}\] Area of plot ABCD = Area of \[\Delta \text{ABC}\] + Area of \[\Delta \text{ACD}\] \[=384+300=684{{m}^{2}}\]