Write a system of equation based on the problem
⇒First equation depicts "the width of her garden is one-third the length"
[tex]w= \frac{1}{3}l[/tex]
[tex]w= \cfrac{l}{3}[/tex]
⇒Second equation depicts "the perimeter is 40 feet"
perimeter = 40
2l + 2w = 40
2(l + w) = 40
l + w = 40/2
l + w = 20
Solve the system of equation, substitute [tex] \cfrac{l}{3} [/tex] as w to the second equation to find the length
l + w = 20
[tex]l+ \dfrac{l}{3}=20 [/tex]
Equalize the denominators
[tex]\dfrac{3l}{3}+ \dfrac{l}{3}=20 [/tex]
[tex]\dfrac{3l}{3}+ \dfrac{l}{3}=20 [/tex]
Simplify the numerators
[tex]\dfrac{4l}{3} =20 [/tex]
4l = 20 × 3
4l = 60
l = 60/4
l = 15
The length is 15 feet
Substitute the value of l to the first equation to find the width
[tex]w= \cfrac{l}{3}[/tex]
[tex]w= \cfrac{15}{3}[/tex]
w = 5
The width is 5 feet
