L=2x-1

W=x+3
Area =294cm
find length and with of rectangle

L * W = area

(2x-1)(x+3) = 294

Solve for x.

To find the length and width of a rectangle when given the area, we can use the formula:

Area = Length * Width

Given the equation for the length: L = 2x - 1, and the equation for the width: W = x + 3, as well as the known area: 294 cm, we can substitute these values into the formula and solve for x.

So, we have:

(2x - 1) * (x + 3) = 294

Expanding the equation, we get:

2x^2 + 6x - x - 3 = 294

This simplifies to:

2x^2 + 5x - 3 = 294

Rearranging the equation, we have:

2x^2 + 5x - 297 = 0

Now, let's solve this quadratic equation to find the value of x using either factoring, completing the square, or the quadratic formula.

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 2, b = 5, and c = -297.

Plugging in these values, we have:

x = (-5 ± √(5^2 - 4 * 2 * -297)) / (2 * 2)

Calculating the discriminant, we get:

x = (-5 ± √(25 + 2376)) / 4

x = (-5 ± √(2401)) / 4

Since √(2401) = 49, we have:

x = (-5 ± 49) / 4

This leads to two possible solutions:

1) x = (-5 + 49) / 4 = 44 / 4 = 11

2) x = (-5 - 49) / 4 = -54 / 4 = -13.5

Since the width of a rectangle cannot be negative, we can discard the second solution.

So, the value of x is 11.

Now, we can substitute this value of x back into the equations for the length and width to get their respective values.

Length (L) = 2x - 1 = 2(11) - 1 = 22 - 1 = 21 cm

Width (W) = x + 3 = 11 + 3 = 14 cm

Therefore, the length of the rectangle is 21 cm and the width is 14 cm.

To find the length and width of the rectangle, we need to solve the given equations.

The first equation represents the length of the rectangle, L, in terms of x: L = 2x - 1.
The second equation represents the width of the rectangle, W, in terms of x: W = x + 3.
The area of a rectangle is given by the formula: Area = Length * Width.

We are given that the area of the rectangle is 294 cm²: Area = 294 cm².

We can substitute the expressions for length and width into the area formula:
(2x - 1) * (x + 3) = 294.

We can solve this quadratic equation by expanding the equation and rearranging it to equal zero:
2x^2 + 5x - 291 = 0.

To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a).

Plugging in the values from our equation, we get:
x = (-(5) ± √((5)^2 - 4(2)(-291))) / (2(2)).

Simplifying this equation, we get:
x = (-5 ± √(25 + 2328)) / 4.

x = (-5 ± √(2353)) / 4.

We can now compute the two possible values of x. Once we have the values of x, we can substitute them back into the equations for length and width to find their values.