Makakuha ng mabilis at eksaktong mga sagot sa IDNStudy.com. Sumali sa aming interactive na platform ng tanong at sagot para sa mabilis at eksaktong tugon mula sa mga propesyonal sa iba't ibang larangan.

a rectangular garden has an area of 84m squared and a perimeter of 38m. Find its length and width.



Sagot :

[tex]area: A = 84 \ m ^2 \\perimeter: \ P = 38 \ m\\length: l = \ ?\\ width : \ w=? \\ \\\begin{cases} A=l\cdot w \\ P=2l+2w \end{cases}\\\\\begin{cases} 84=l\cdot w \\ 38=2l+2w \ \ /:2 \end{cases}[/tex]

[tex]\begin{cases} 84=l\cdot w \\ 19= l+ w \end{cases}\\ \\ \begin{cases} 84=l\cdot w \\ l=19-w \end{cases}\\\\ substitution\\\\84 =l\cdot w \\84=(19-w)w\\84=19w-w^2[/tex]

[tex]w^2-19w+84=0\\\\a=1, \ \ b=-19,\ \ c=84 \\\\\\Delta =b^2-4ac = (-19)^2 -4\cdot1\cdot 84 = 361-336=25 \\ \\w_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{19-\sqrt{25}}{2 }=\frac{ 19-5}{2}=\frac{14}{2}=7[/tex]

[tex]w_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{19+\sqrt{25}}{2 }=\frac{ 19+5}{2}=\frac{24}{2}=12 \\ \\\begin{cases}w_{1}= 7\\ 84 = w_{1}\cdot l_{1} \end{cases}\ \ or \ \ \begin{cases}w_{2}= 12\\84 =w_{2}\cdot l_{2} \end{cases} \\\\\begin{cases}w_{1}= 7\\84=7\cdot l_{1}\ \ /:7 \end{cases}\ \ or \ \ \begin{cases}1= 12\\84=12\cdot l_{2} \ \ / :12 \end{cases}\\ \\ \begin{cases}w_{1}= 7\\ l_{1}= \frac{84}{7} \end{cases}\ \ or \ \ \begin{cases}1= 12\\ l_{2}= \frac{84}{12} \end{cases}[/tex]

[tex]Answer : \ \begin{cases}w_{1}= 7\\ l_{1}= 12 \end{cases}\ \ or \ \ \begin{cases}1= 12\\ l_{2}= 7 \end{cases}[/tex]