a large rectangular movie screen in an IMAX theater has an area of 8624 square feet. Find the dimensions of the screen if it is 10 feet longer than it is wide.

w(w+10) = 8624

w = 88

w=88

To find the dimensions of the large rectangular movie screen, we'll set up an equation based on the given information.

Let's assume the width of the screen is "x" feet. Therefore, the length of the screen will be "x + 10" feet, since it is 10 feet longer than its width.

The area of a rectangle is calculated by multiplying its width by its length. In this case, we have:

Area = Width x Length

8624 = x * (x + 10)

To solve this equation, we'll first multiply the terms inside the parentheses:

8624 = x^2 + 10x

Next, we'll rearrange the equation to bring all the terms to one side:

x^2 + 10x - 8624 = 0

To solve this quadratic equation, we can either use factoring or the quadratic formula. Since factoring may not give us integer solutions in this case, we'll use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Here, a = 1, b = 10, and c = -8624. Substituting these values into the formula:

x = (-10 ± sqrt(10^2 - 4(1)(-8624))) / (2(1))

Simplifying further:

x = (-10 ± sqrt(100 + 34496)) / 2

x = (-10 ± sqrt(34596)) / 2

Using a calculator, we can find the square root of 34596:

x ≈ (-10 ± 186) / 2

Simplifying:

x ≈ (176 / 2) or (-206 / 2)

Therefore, the possible widths of the large rectangular movie screen are approximately:

x ≈ 88 or -103

Since dimensions cannot be negative, we discard the negative value.

Hence, the width of the screen is approximately 88 feet. Consequently, the length can be found by adding 10 feet:

Length = Width + 10 = 88 + 10 = 98 feet

Therefore, the dimensions of the large rectangular movie screen are approximately 88 feet by 98 feet.