Question

The length of a rectangle is less than three times the width, and the area of the rectangle is . Find the dimensions of the rectangle.

Answer 1

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

`\begin{gathered} A=l* 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=(-7)/(3)(invalid) \\ OR \\ w-4=0 \\ w=4 \end{gathered}`

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