Math homework college

Question

A large rectangular movie screen in an IMAX theater has an area of 6,624 square feet. Find the dimensions of the screen if it is 20 feet longer than it is wide.

length	ft
width	ft

Answer 1

20 + x represents the length, and x represents the width. We multiply these dimensions to get the area, which equals 6624. So x(x + 20) = 6624. Next, distribute the x. So, x squared + 20x = 6624. Next, we subtract 6624 from both sides to get the quadratic in standard form. x squared + 20x - 6624 = 0. Now, we can factor or use the quadratic formula to solve for x. Since 6624 is such a large number, I think factoring may take longer. So, I use the quadratic formula. x = (-b plus or minus square root of( b squared - 4ac) all divided by 2a. a = 1, b = 20, and c = -6624. After plugging in these values into the formula, we end up with the following:

(-20 plus or minus the square root of ((20 squared) - 4(1)(-6624)) all divided by 2. We end up with (-20 plus or minus 164)/2. We disregard the negative value (-92) because we can't have negative dimensions. The positive value is 72. Finally, the length equals 20 +72, which is 92ft, and the width is 72 ft.