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Question Number 33805 by pieroo last updated on 25/Apr/18

$$\mathrm{The}\mathrm{perimeter}\mathrm{of}\mathrm{a}\mathrm{square}\mathrm{and}\mathrm{a}\mathrm{rectangle}\mathrm{is}\mathrm{the}$$$$\mathrm{same}.\mathrm{The}\mathrm{width}\mathrm{of}\mathrm{the}\mathrm{rectangle}\mathrm{is}6\mathrm{cm}\mathrm{and}\mathrm{its}\mathrm{area}$$$$\mathrm{is}16{\mathrm{cm}}^2\mathrm{less}\mathrm{than}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{square}.\mathrm{Find}\mathrm{the}$$$$\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{square}.$$

Answered by MJS last updated on 25/Apr/18

$$\mathrm{square}=a\times a$$$$\mathrm{rectangle}=6\times b$$$$$$$$6b+16=a^2$$$$4a=2b+12\Rightarrow b=2a-6$$$$$$$$6(2a-6)+16=a^2$$$$12a-20=a^2$$$$a^2-12a+20=0$$$$(a-2)(a-10)=0$$$$a_1=2\Rightarrow b_1=2a_1-6=-2\mathrm{not}\mathrm{valid}$$$$a_2=10\Rightarrow b_2=2a_2-6=14$$$$\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{square}=a_2^2=100{cm}^2$$

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