A) 60 cm
B) 40 cm
C) 15 cm
D) 30 cm
E) None of these
Correct Answer: D
Solution :
Explanation Let the small sides are 4x and 3x. From the figure \[{{\operatorname{BC}}^{2}}=A{{B}^{2}}=A{{C}^{2}}\] (Pythagoras theorem) \[\Rightarrow \,\,\,\,{{\operatorname{BC}}^{2}}= {{\left( 3x \right)}^{2}}+ 4{{x}^{2}}\] \[\Rightarrow \,\,\,{{\operatorname{BC}}^{2}}= 9{{x}^{2}}+ 16{{x}^{2}}\] \[\Rightarrow \,\,\,{{\operatorname{BC}}^{2}}= 25{{x}^{2}}BC = 5x\] According to question, \[\operatorname{Length} of rectangle = 5x\] Breadth of rectangle \[\Rightarrow \,\,\,\frac{4}{5}\times 5x\,\,=\,\,4x\] Perimeter of rectangle \[= \,2\left( 5x +4x \right) = 18x\] \[\Rightarrow \,\,\,\,18x = 180 cm\] \[\Rightarrow \,\,\,x= 10\,\,cm\] The length of shortest side \[= 3 \times 10 = 30 cm.\]You need to login to perform this action.
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