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 2w² + 4w = 240 2w² + 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

Set each factor equal to zero from $2(w + 12)(w - 10)=0$. We get $w+12 = 0$ or $w - 10=0$. Solving $w+12 = 0$ gives $w=- 12$, and solving $w - 10=0$ gives $w = 10$. Since width cannot be negative, the width $w = 10$ cm.

Step2: Solve for length

The length is given by $l=2w + 4$. Substitute $w = 10$ into the length - formula: $l=2\times10+4=24$ cm.

Answer:

Width: 10 cm
Length: 24 cm