A) 54 sqm
B) 56.5 sqm
C) 57 sqm
D) none of these
Correct Answer: A
Solution :
[a] Let the sides of triangle are 3x, 4x and 5x respectively. \[\therefore \] Perimeter\[\text{=3}x+4x+5x=12x\] \[\therefore \] \[12x=36\](Given) So sides are 9 cm, 12 cm and 15 cm The sides follow the relation \[{{15}^{2}}={{12}^{2}}+{{9}^{2}}\] \[\therefore \] Triangle is a right angled triangle. \[\therefore \] Area of \[\Delta =\frac{1}{2}\times 9\times 12=54\,\,c{{m}^{2}}\] Area can also be calculated using Heron?s formula \[s=\frac{9+12+15}{2}=18\,\,cm\] \[\therefore \]Area\[=\sqrt{18(18-9)(18-12)(18-15)}\]\[=\sqrt{18\times 9\times 6\times 3}=\sqrt{9\times 2\times 9\times 3\times 2\times 3}\] Area\[=9\times 2\times 3=54\,\,c{{m}^{2}}\]
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