How do I solve this equation? The room is 3 ft longer than twice the width. The see is 495 sq ft.

Question

Please help me solve the question. The length of the classroom is 3 ft longer than twice it's width.  The area is 495 sq ft. Write the equation the shows the area.

Answer 1

Let W = width and L = length

L = 2W +3 is the math equivalent of "the room is 3 feet longer than twice the width

Area = length * width = L * W = (2W + 3) * W = 495

Expand and collect terms: 2W² + 3W - 495 = 0

Use the quadratic formula to get an extraneous root and W = 15 which makes L = 33.

Check these results to make sure the area is correct.

Answer 2

w(2w+3) = 495

 

2w^2 + 3w - 495 = 0

 

(2w   +  33)(w  -   15  ) = 0

 

2w+33 results in negative measurements;

 

w-15 = 0 ---> w = 15

 

2(15)+3 = 33 is the length