Question

A rectangular shaped garden is 2 feet longer than the width. If its area is 143 sq. feet, find the dimensions.Width = 13 feet and length = 15 feetWidth = 11 feet and length = 9 feetWidth = 11 feet and length = 13 feetWidth = 13 feet and length = 11 feet

Answer 1

Step-by-step explanation

From the statement, we have a rectangular-shaped garden that:

• has a width ,w,,

,

• has a length ,l = w + 2ft,,

,

• an area ,A = 143 ft²,.

The area of a rectangle is given by:

`A=w\cdot l.`

(1) Replacing the data from above, we have:

`143ft^2=w\cdot(w+2ft).`

Rewriting this equation, we get:

`\begin{gathered} 143ft^2=w^2+2ft\cdot w, \\ w^2+2ft\cdot w-143ft^2, \\ w^2+2w-143=0. \end{gathered}`

In the last equation, we have omitted the units.

(2) We know that the roots of a 2nd order polynomial equation:

`a\cdot w^2+b\cdot w+c=0.`

Are given by the formula:

`w_(\pm)=(-b\pm√(b^2-4ac))/(2a).`

We identify the coefficients:

• a = 1,

,

• b = 2,

,

• c = -143.

Replacing these coefficients in the formula above, we get:

`\begin{gathered} w_+=(-2+√(2^2-4\cdot2\cdot(-143)))/(2\cdot1)=11, \\ w_-=(-2-√(2^2-4\cdot2\cdot(-143)))/(2\cdot1)=-13. \end{gathered}`

Because w is the width, it can only take positive values, so we conclude that:

`w=11.`

Replacing this value in the equation for the length, we get:

`l=11ft+2ft=13ft.`Answer

Width = 11 ft and length = 13 ft