Question

a rectangles length is 4 more than twice its width, its area is 240 square centimeters.
complete the work to find the dimensions of the rectangle.
$w(2w + 4) = 240$
$2w^2 + 4w = 240$
$2w^2 + 4w - 240 = 0$
$2(w + 12)(w - 10) = 0$
what is the width of the rectangle?
what is the length of the rectangle?

Explanation:

Step1: Solve for width \( w \)

Given the equation \( 2(w + 12)(w - 10)=0 \). We set each factor equal to zero:

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

Step2: Find the length

The length is given by \( 2w + 4 \). Substitute \( w = 10 \):
\( 2(10)+4=20 + 4=24 \).

Answer:

Width: \( 10 \) centimeters
Length: \( 24 \) centimeters