Question

final exam
the length of a rectangle is 4 meters less than twice the width. if the area of the rectangle is 240 square meters, find the dimensions.
the width is □ meters.
the length is □ meters.
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Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) meters. Then the length \( l \) is \( 2w - 4 \) meters (since length is 4 meters less than twice the width).

Step2: Use area formula

The area of a rectangle is \( A = l \times w \). We know \( A = 240 \), so substitute \( l = 2w - 4 \) into the formula:

$$ 240 = (2w - 4) \times w $$

Expand the right side:

$$ 240 = 2w^2 - 4w $$

Rearrange into standard quadratic form:

$$ 2w^2 - 4w - 240 = 0 $$

Divide all terms by 2 to simplify:

$$ w^2 - 2w - 120 = 0 $$

Step3: Solve the quadratic equation

Factor the quadratic: \( w^2 - 2w - 120 = (w - 12)(w + 10) = 0 \)
Set each factor equal to zero:

• \( w - 12 = 0 \) gives \( w = 12 \)
• \( w + 10 = 0 \) gives \( w = -10 \) (discard since width can't be negative)

Step4: Find the length

Substitute \( w = 12 \) into \( l = 2w - 4 \):
\( l = 2(12) - 4 = 24 - 4 = 20 \)

Answer:

The width is \( \boldsymbol{12} \) meters.
The length is \( \boldsymbol{20} \) meters.