Mathematics

# The length of a swimming pool is 8m longer than its width and the area is 105m2

$width : w \\ length : \ l = w + 8 \\ A = 105 \ m^2 \\ \\A= w \cdot l \\ \\w(w+l)=105 \\ \\w^2+w = 105 \\ \\w^2+w-105 =0 \\ \\(w+15)(w-7)=0 \\ \\w+15 =0 \ \ or \ \ w-7 = 0 \\ \\w = -15 \ \ or \ \ w=7 \\ \\ width \ cant \ be \ negative, \ so \\ \\ w = 7 \ and \ l = w+8 = 7 +8 =15 \\ \\chek : \\ \\ A=w\cdot l \\ \\A=7\cdot 15=105 \ m^2$
$l\ \rightarrow\ the\ length\\w\ \rightarrow\ the\ width \\\\l=w+8\ \ \ and\ \ \ l\cdot w=105\ \ \ and\ \ \ l>0,\ w>0\\\\(w+8)\cdot w=105\ \ \ \Rightarrow\ \ \ w^2+8w=105\\\\ w^2+2\cdot4w+4^2=105+4^2\\\\ (w+4)^2=105+16\ \ \ \Rightarrow\ \ \ (w+4)^2=121\\\\w+4=11\ \ \ or\ \ \ w+4=-11\\\\w=7\ \ \ \ \ \ \ \ \ \ or\ \ \ w=-15<0\\\\w=7\ \ \ \Rightarrow\ \ \ l=7+8=15\\\\Ans.\ the\ length\ is\ 15\ m\ \ and\ \ the\ width\ is\ 7\ m.$