Lisa is cutting carpet for a rectangular room. The area of the room is 324ft^2 . The length of the room is 3 feet longer than twice he width. What should the dimensions of he carpet be?

w(2w+3) = 324

2w^2+3w-324 = 0
(2w+27)(w-12) = 0

w=12, so the room is 12x27

The Oldham's living room is a rectangle measuring 19ft by 20ft. What is the area?

To find the dimensions of the carpet, we need to solve the given equations. Let's denote the width of the room as "w" in feet.

Given:
Area of the room = 324 ft²
Length of the room = 3 feet longer than twice the width

The formula for the area of a rectangle is length × width.

Area of the room = Length × Width
324 = (2w + 3) × w

To solve this equation, let's multiply it out and rearrange:

324 = 2w² + 3w

Now, let's subtract 324 from both sides to simplify the equation:

2w² + 3w - 324 = 0

This is a quadratic equation. To solve it, we can either factorize it or use the quadratic formula. In this case, factoring is more complicated, so we'll use the quadratic formula:

w = (-b ± √(b² - 4ac)) / (2a)

Here, a = 2, b = 3, and c = -324. Substituting the values into the formula:

w = (-(3) ± √((3)² - 4(2)(-324))) / (2(2))

Simplifying:

w = (-3 ± √(9 + 2592)) / 4
w = (-3 ± √(2601)) / 4
w = (-3 ± 51) / 4

Now, let's calculate the two possible values of w:

w₁ = (-3 + 51) / 4 = 12
w₂ = (-3 - 51) / 4 = -13.5

Since the width of a room cannot be negative, we discard the negative value.

Therefore, the width of the room (w) is 12 feet.

Now, we can find the length of the room:

Length = 2w + 3
Length = 2(12) + 3
Length = 27 feet

So, the dimensions of the carpet should be 12 feet (width) by 27 feet (length).