Given
A rectangle garden has a width of 90 feet. the perimeter is 500 feet.
We are to solve for the length of the garden
[tex]The\text{Perimeter of a rectangle =2(L+W)}[/tex]Where L is the length and
W is the width
From the question
W = 90 feet
P = 500 feet
[tex]\begin{gathered} P\text{ =2(L +W)} \\ 500=2(L+90) \end{gathered}[/tex][tex]\begin{gathered} 500=2(L+90) \\ \text{open the bracket} \\ 500=2L+180 \\ \text{collect the like terms} \\ 500-180=2L \\ 320=2L \\ \text{Divide both sides by 2} \\ \frac{320}{2}=\frac{2l}{2} \\ \\ L=160\text{ ft} \end{gathered}[/tex]Another way
[tex]\begin{gathered} P=2(L+W) \\ P=500ft\text{ and W=90ft} \\ 500=(2\times L\text{ )}+(2\times90) \\ \\ 500=2L+180 \\ \text{collect like terms} \\ 500-180=2l \\ 320=2l \\ \text{divide both sides by 2} \\ \frac{320}{2}=\frac{2l}{2} \\ \\ 160=l \end{gathered}[/tex]The length of the garden is 160 feet
