Question

the length of a rectangle is 6 kilometers less than twice its width. if its area is 56 square kilometers, find the dimensions of the rectangle and give the equation required to solve. 7 km x 8 km w(2w + 6)=56 14 km x 4 km 2w(w - 6)=56 7 km x 8 km w(w - 6)=56 7 km x 8 km w(2w - 6)=56

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) kilometers. Then the length \( l = 2w - 6 \) kilometers.

Step2: Use the area formula

The area of a rectangle is \( A=l\times w \). Substituting \( l = 2w - 6 \) and \( A = 56 \), we get \( w(2w - 6)=56 \).

Step3: Solve the equation (optional for verification)

Expand \( w(2w - 6)=56 \) to \( 2w^{2}-6w - 56 = 0 \), then divide by 2: \( w^{2}-3w - 28 = 0 \). Factor: \( (w - 7)(w + 4)=0 \). So \( w=7 \) (width can't be negative). Then \( l=2\times7 - 6=8 \).

Answer:

\( 7\mathrm{km}\times8\mathrm{km} \) with the equation \( w(2w - 6)=56 \)