QuestionAugust 25, 2025

The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 336 square meters, find the dimensions. The width is square square and the length is square square

The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 336 square meters, find the dimensions. The width is square square and the length is square square
The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 336 square meters, find the dimensions. The width is square square and the length is square square

Solution
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Answer

The width is 14 meters and the length is 24 meters. Explanation 1. Define variables Let width be w and length be 2w - 4. 2. Set up area equation Area = width \times length, so w(2w - 4) = 336. 3. Solve quadratic equation Expand: 2w^2 - 4w = 336. Rearrange: 2w^2 - 4w - 336 = 0. Divide by 2: w^2 - 2w - 168 = 0. 4. Factor the quadratic Factor: (w - 14)(w + 12) = 0. Solutions: w = 14 or w = -12. 5. Select positive solution Width must be positive, so w = 14. 6. Calculate length Length = 2w - 4 = 2(14) - 4 = 24.

Explanation

1. Define variables<br /> Let width be $w$ and length be $2w - 4$.<br />2. Set up area equation<br /> Area = width $\times$ length, so $w(2w - 4) = 336$.<br />3. Solve quadratic equation<br /> Expand: $2w^2 - 4w = 336$. Rearrange: $2w^2 - 4w - 336 = 0$. Divide by 2: $w^2 - 2w - 168 = 0$.<br />4. Factor the quadratic<br /> Factor: $(w - 14)(w + 12) = 0$. Solutions: $w = 14$ or $w = -12$.<br />5. Select positive solution<br /> Width must be positive, so $w = 14$.<br />6. Calculate length<br /> Length = $2w - 4 = 2(14) - 4 = 24$.
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