SOLUTION:
Case: Area of rectangles
Method:
Let the width be 'w'
The length, 'l' is 5 yards less than three times the width.
Hence,
l = 3w - 5
Since the Area, A = 28 sq yards
[tex]\begin{gathered} A=l\times w \\ 28=(3w-5)w \\ 28=3w^2-5w \\ 3w^2-5w-28=0 \\ 3w^2-12w+7w-28=0 \\ 3w(w-4)+7(w-4)=0 \\ (3w+7)(w-4)=0 \\ 3w+7=0 \\ 3w=-7 \\ w=\frac{-7}{3}(invalid) \\ OR \\ w-4=0 \\ w=4 \end{gathered}[/tex]
If the width w= 4 yards
Hence,
l = 3w - 5
l = 3(4) -5
l = 12 - 5
l = 7 yards
Final answer:
Length : 7 yd
Width : 4 yd
