The ratio of the perimeter of square \[STUV\]to that of\[\Delta PQR\]is\[4:3\]. What is the area of the square?
A) \[23.04\,\,{{m}^{2}}\]
B) \[25.6\,\,{{m}^{2}}\]
C) \[40.96\,\,{{m}^{2}}\]
D) \[655.36\,\,{{m}^{2}}\]
Correct Answer: C
Solution :
According to the given problem, \[PR=RQ=1.5\times 4.8\,\,m=7.2\,\,m\] Perimeter of\[\Delta PQR=(2\times 7.2+4.8)m\] \[=19.2\,\,m\] Ratio of perimeter of the square and the triangle \[=4:3\] Perimeter of square\[=\frac{19.2}{3}\times 4=25.6\,\,m\] \[\therefore \]Side of the square\[=\frac{25.6}{4}m=6.4\,\,m\] Hence, area of the square\[=6.4\times 6.4\,\,{{m}^{2}}\] \[=40.96\,\,{{m}^{2}}\]
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