A large rectangular movie screen in an IMAX theater has an area of 7200 square feet. Find the dimensions of the screen if it is 10 feet longer than the width.

Try (x+10)(x)=7200.

To find the dimensions of the screen, we can use the given information about the area and the relationship between its length and width.

Let's assume:
Length = L
Width = W

We are given that the area of the screen is 7200 square feet, so we have the equation:
L x W = 7200

Additionally, we are given that the length is 10 feet longer than the width:
L = W + 10

We can substitute this equation for L in the previous equation to solve for the dimensions.

Substituting L in terms of W, we have:
(W + 10) x W = 7200

Expanding the equation:
W^2 + 10W = 7200

Rearranging the equation to quadratic form:
W^2 + 10W - 7200 = 0

Now, we can solve this quadratic equation to find the values of W.

We can either factorize the equation or use the quadratic formula to find the values of W. Since factorizing may be difficult in this case, we'll use the quadratic formula.

The quadratic formula states that for an equation in the form of Ax^2 + Bx + C = 0, the solutions for x are given by:
x = (-B ± sqrt(B^2 - 4AC)) / 2A

For our equation W^2 + 10W - 7200 = 0:
A = 1
B = 10
C = -7200

Plugging in these values into the quadratic formula, we have:
W = (-10 ± sqrt(10^2 - 4(1)(-7200))) / (2(1))

Simplifying further:
W = (-10 ± sqrt(100 + 28800)) / 2
W = (-10 ± sqrt(28900)) / 2
W = (-10 ± 170) / 2

So we have two possible values for W:
W1 = (-10 + 170) / 2 = 160 / 2 = 80
W2 = (-10 - 170) / 2 = -180 / 2 = -90

Since the width cannot be negative in this case, we disregard the second value.

Now that we have the width, we can find the length using the equation L = W + 10:
L = 80 + 10 = 90

Therefore, the dimensions of the screen are:
Width = 80 feet
Length = 90 feet