Answer:
240 square yards
Step-by-step explanation:
Let's denote the length of the rectangle as [tex]L[/tex] (in yards) and the width as [tex]W = 12[/tex] yards. The formula for the perimeter ([tex]P[/tex]) of a rectangle is given by:
[tex] P = 2L + 2W [/tex]
Given that the perimeter is 64 yards, we can set up the equation:
[tex] 64 = 2L + 2 \times 12 [/tex]
Simplify the equation:
[tex] 64 = 2L + 24 [/tex]
Subtract 24 from both sides:
[tex] 64-24 = 2L + 24-24 [/tex]
[tex] 40 = 2L [/tex]
Divide by 2:
[tex]\dfrac{ 40}{2} =\dfrac{ 2L}{2} [/tex]
[tex] L = 20 [/tex]
Now that we have the length [tex]L[/tex] (20 yards) and the width [tex]W[/tex] (12 yards), we can find the area ([tex]A[/tex]) of the rectangle using the formula:
[tex] A = L \times W [/tex]
[tex] A = 20 \times 12 [/tex]
[tex] A = 240 \, \textsf{square yards} [/tex]
Therefore, the area of the rectangle is [tex]240[/tex] square yards.
