Answer:
Message ko nlang Sayo ayaw icopy
Step-by-step explanation:
\begin{gathered}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}\end{gathered}
area:A=84 m
2
perimeter: P=38 m
length:l= ?
width: w=?
{
A=l⋅w
P=2l+2w
{
84=l⋅w
38=2l+2w /:2
\begin{gathered}\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\end{gathered}
{
84=l⋅w
19=l+w
{
84=l⋅w
l=19−w
substitution
84=l⋅w
84=(19−w)w
84=19w−w
2
\begin{gathered}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\end{gathered}
w
2
−19w+84=0
a=1, b=−19, c=84
Delta=b
2
−4ac=(−19)
2
−4⋅1⋅84=361−336=25
w
1
=
2a
−b−
Δ
=
2
19−
25
=
2
19−5
=
2
14
=7
\begin{gathered}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}\end{gathered}
w
2
=
2a
−b+
Δ
=
2
19+
25
=
2
19+5
=
2
24
=12
{
w
1
=7
84=w
1
⋅l
1
or {
w
2
=12
84=w
2
⋅l
2
{
w
1
=7
84=7⋅l
1
/:7
or {
1=12
84=12⋅l
2
/:12
{
w
1
=7
l
1
=
7
84
or {
1=12
l
2
=
12
84
\begin{gathered}Answer : \ \begin{cases}w_{1}= 7\\ l_{1}= 12 \end{cases}\ \ or \ \ \begin{cases}1= 12\\ l_{2}= 7 \end{cases}\end{gathered}
Answer: {
w
1
=7
l
1
=12
or {
1=12
l
2
=7
