the length of a photograph is 1 cm less than twice the width. The area is 45 cm^2. Find the dimensions of the photograph.

To find the dimensions of the photograph, we need to set up equations using the given information.

Let's assume that the width of the photograph is x cm.

According to the given information, the length of the photograph is 1 cm less than twice the width. This can be written as:

Length = 2x - 1 cm

The area of a rectangle is given by the formula: Area = Length × Width.

We are given that the area of the photograph is 45 cm², so we can set up an equation as:

45 = (2x - 1) × x

Now, let's solve the equation to find the value of x (width).

45 = 2x² - x

2x² - x - 45 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -1, and c = -45. Plugging these values into the quadratic formula, we get:

x = (-(-1) ± √((-1)² - 4(2)(-45))) / (2(2))

x = (1 ± √(1 + 360)) / 4

Simplifying further:

x = (1 ± √361) / 4

x = (1 ± 19) / 4

Therefore, we have two possible values for x:

x1 = (1 + 19) / 4 = 20 / 4 = 5 cm (Taking the positive value)

x2 = (1 - 19) / 4 = -18 / 4 = -4.5 cm (Taking the negative value is not meaningful in this context)

So, the width of the photograph is 5 cm.

To find the length, we can substitute this width value into the expression for the length:

Length = 2x - 1 = 2(5) - 1 = 10 - 1 = 9 cm

Therefore, the dimensions of the photograph are:

Width = 5 cm
Length = 9 cm

L = 2W - 1

L * W = (2W-1) * W = 45

Solve for W, then L.