question_answer

A Square lawn has a 2m wide path surrounding it. If the area of the path is\[136\,\,{{m}^{2}}\]. Find the area of the lawn.

A) \[225\,\,{{m}^{2}}\]                

B) \[220\,\,{{m}^{2}}\]

C) \[330\,\,{{m}^{2}}\]                

D) \[340\,\,{{m}^{2}}\]

Correct Answer: A

Solution :

Area of path \[=(x\times 2+x\times 2+x\times 2+x\times 2+4+4+4+4){{m}^{2}}\] \[=(2x+2x+2x+16)\,{{m}^{2}}\] \[=(8x+16x){{m}^{2}}=136\,\,{{m}^{2}}\] \[8x=120\,\,{{m}^{2}}\] \[x=15\,\,m\] \[{{x}^{2}}=225\,\,c{{m}^{2}}\]