Question

A huge suspended LED screen is the centerpiece of The Place, a popular mall in Beijing, China. Find the length and width of a similar rectangular screen if the length is 5 meters more than 6 times its width, and the viewable area is 9,800 square meters.

Answer 1

Let's assume the width of the screen is "x" meters.

Then the length is "6x+5" meters.

The area of the rectangle = length x width

9800 = (6x+5) x x

9800 = 6x^2 + 5x

By rearranging the equation, we get:

6x^2 + 5x - 9800 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. Using the quadratic formula, we get:

x = [-5 ± sqrt(5^2 - 4(6)(-9800))] / (2*6)

x = [-5 ± sqrt(192005)] / 12

Since the width cannot be negative, we take the positive value:

x = (sqrt(192005) - 5) / 12

x ≈ 21.35 meters (rounded to two decimal places)

So, the length of the screen is:

6x+5 = 6(21.35) + 5

= 128.1 meters (rounded to one decimal place)

Therefore, the length and width of a similar rectangular screen would be approximately 128.1 meters by 21.35 meters, respectively.

Explanation: