The length of a rectangle is \( 3 \mathrm{~m} \) less than twice the width, and the area of the rectangle is \( 14 \mathrm{~m}^{2} \). Find the dimensions of the rectangle.
Answer
5. The dimensions of the rectangle are approximately \( 2.8823 \mathrm{~m} \) width and \( 2.7646 \mathrm{~m} \) length.
Step 1 ：1. Let width of rectangle be \( w \mathrm{~m} \), so length \( = (2w - 3) \mathrm{~m} \).
Step 2 ：2. Area of rectangle is \( 14 \mathrm{~m}^{2} \), so equation is \( w(2w - 3) = 14 \).
Step 3 ：3. Solve quadratic equation \( 2w^2 - 3w - 14 = 0 \) with quadratic formula to get \( w \approx 2.8823 \mathrm{~m} \).
Step 4 ：4. Calculate the length \( = (2w - 3) = (2(2.8823) - 3) \approx 2.7646 \mathrm{~m} \).
Step 5 ：5. The dimensions of the rectangle are approximately \( 2.8823 \mathrm{~m} \) width and \( 2.7646 \mathrm{~m} \) length.
